Category Archives: Quantum Physics

Neutrinos are known for funny business. Now scientists have set a new limit on a quantum trait responsible for the subatomic particles quirkiness: uncertainty.

The lightweight particles morph from one variety of neutrino to another as they travel, a strange phenomenon calledneutrino oscillation(SN: 10/6/15). That ability rests on quantum uncertainty, a sort of fuzziness intrinsic to the properties of quantum objects, such as their location or momentum. But despite the importance of quantum uncertainty, the uncertainty in the neutrinos position has never been directly measured.

The quantum properties of the neutrino stuff is a little bit of the Wild West at the moment, says nuclear physicist Kyle Leach of Colorado School of Mines in Golden. Were still trying to figure it out.

Its impossible to know everything about a quantum particle.Heisenbergs uncertainty principlefamously states that its futile to attempt to precisely determine both the momentum of a quantum object and its position (SN: 1/12/22). Now, Leach and colleagues report new details about the size of the neutrinos wave packet, which indicates the uncertainty in the particles position.

Quantum particles travel as waves, with ripples that are related to the probability of finding a particle at a given location. A wave packet is the set of ripples corresponding to a single particle. The new experimentsets a limit on the size of the wave packetfor neutrinos produced in a particular type of radioactive decay, Leachs team reports in a paper submitted April 3 to arXiv.org. The particles have a wave packet size of at least 6.2 trillionths of a meter.

The researchers studied neutrinos produced in the decay of beryllium-7, via a process called electron capture. In this process, a beryllium-7 nucleus absorbs an electron, and the atom transforms into lithium-7 and spits out a neutrino.

The team implanted beryllium-7 atoms in a highly sensitive device made from five layers of material, including superconducting tantalum, which can transmit electricity without resistance. In the decay, the newly produced lithium-7 recoils away from the neutrino. When cooled to 0.1 degrees above absolute zero (273.05 Celsius), the device allowed the researchers to detect the energy of that recoil. The spread in the energy of the lithium atoms revealed the neutrino wave packets minimum size.

Neutrinos are special in that they interact so rarely with matter that they maintain their quantum properties over long distances. Most quantum effects take place on very small scales, but neutrino oscillations occur over thousands of kilometers.

So studying the size of neutrinos wave packets could help unveil the connection between the everyday world of classical physics and the strangeness of quantum physics, says Benjamin Jones, a neutrino physicist at the University of Texas at Arlington who was not involved with the experiment. If you can predict something like this and then measure it, then you really validate some of the ideas that people have about how the classical world emerges from an underlying quantum reality, he says. And thats what really got me excited about this in the first place.

In another study, submitted April 30 to arXiv.org, Jones and his colleaguestheoretically predicted the size of the neutrino wave packet, pegging it at about 2.7 billionths of a meter. Now its up to experimental physicists to try to measure it, not just determine its minimum size.

Measuring the size of neutrinos wave packets might help resolve discrepancies among past experiments, and potentially point the way to new types of subatomic particles still to be discovered. But the size of the neutrinos wave packet depends on how the particle is produced. So its not clear how the size limit observed in Leachs study might translate to neutrinos produced by other means, says neutrino physicist Carlos Argelles of Harvard University. For example, many experiments observe neutrinos from nuclear reactors, but those are produced via a different type of radioactive decay.

Still, Argelles says, the study of the neutrino wave packet has fundamental implications in the quantumness of the neutrino, and the quantumness of the neutrino is actually what makes neutrinos interesting. Its the most unique property that they have.

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The neutrino's quantum fuzziness is beginning to come into focus - Science News Magazine

Researchers have developed a new method called wavefunction matching to tackle the sign problem in Monte Carlo simulations, a common issue in quantum many-body physics. By simplifying the interaction model and using perturbation theory for corrections, this method has proven effective in accurately calculating nuclear properties like mass and radius. It holds promise for broader applications in quantum computing and other fields. Credit: Prof. Serdar Elhatisari

Strongly interacting systems are crucial in the fields of quantum physics and quantum chemistry. Monte Carlo simulations, a type of stochastic method, are widely used to study these systems. However, they face challenges when dealing with sign oscillations. An international team of researchers from Germany, Turkey, the USA, China, South Korea, and France has addressed this issue by developing a new technique called wavefunction matching.

As an example, the masses and radii of all nuclei up to mass number 50 were calculated using this method. The results agree with the measurements, the researchers now report in the journal Nature.

All matter on Earth consists of tiny particles known as atoms. Each atom contains even smaller particles: protons, neutrons, and electrons. Each of these particles follows the rules of quantum mechanics. Quantum mechanics forms the basis of quantum many-body theory, which describes systems with many particles, such as atomic nuclei.

One class of methods used by nuclear physicists to study atomic nuclei is the ab initio approach. It describes complex systems by starting from a description of their elementary components and their interactions. In the case of nuclear physics, the elementary components are protons and neutrons. Some key questions that ab initio calculations can help answer are the binding energies and properties of atomic nuclei and the link between nuclear structure and the underlying interactions between protons and neutrons.

However, these ab initio methods have difficulties in performing reliable calculations for systems with complex interactions. One of these methods is quantum Monte Carlo simulations. Here, quantities are calculated using random or stochastic processes. Although quantum Monte Carlo simulations can be efficient and powerful, they have a significant weakness: the sign problem. It arises in processes with positive and negative weights, which cancel each other. This cancellation leads to inaccurate final predictions.

A new approach, known as wavefunction matching, is intended to help solve such calculation problems for ab initio methods. This problem is solved by the new method of wavefunction matching by mapping the complicated problem in a first approximation to a simple model system that does not have such sign oscillations and then treating the differences in perturbation theory, says Prof. Ulf-G. Meiner from the Helmholtz Institute for Radiation and Nuclear Physics at the University of Bonn and from the Institute of Nuclear Physics and the Center for Advanced Simulation and Analytics at Forschungszentrum Jlich.

As an example, the masses and radii of all nuclei up to mass number 50 were calculated and the results agree with the measurements, reports Meiner, who is also a member of the Transdisciplinary Research Areas Modeling and Matter at the University of Bonn.

In quantum many-body theory, we are often faced with the situation that we can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions cause severe computational problems, says Dean Lee, Professor of Physics from the Facility for Rare Istope Beams and Department of Physics and Astronomy (FRIB) at Michigan State University and head of the Department of Theoretical Nuclear Sciences.

Wavefunction matching solves this problem by removing the short-distance part of the high-fidelity interaction and replacing it with the short-distance part of an easily calculable interaction. This transformation is done in a way that preserves all the important properties of the original realistic interaction. Since the new wavefunctions are similar to those of the easily computable interaction, the researchers can now perform calculations with the easily computable interaction and apply a standard procedure for handling small corrections called perturbation theory.

The research team applied this new method to lattice quantum Monte Carlo simulations for light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. Using precise ab initio calculations, the results closely matched real-world data on nuclear properties such as size, structure, and binding energy. Calculations that were once impossible due to the sign problem can now be performed with wavefunction matching.

While the research team focused exclusively on quantum Monte Carlo simulations, wavefunction matching should be useful for many different ab initio approaches. This method can be used in both classical computing and quantum computing, for example, to better predict the properties of so-called topological materials, which are important for quantum computing, says Meiner.

Reference: Wavefunction matching for solving quantum many-body problems by Serdar Elhatisari, Lukas Bovermann, Yuan-Zhuo Ma, Evgeny Epelbaum, Dillon Frame, Fabian Hildenbrand, Myungkuk Kim, Youngman Kim, Hermann Krebs, Timo A. Lhde, Dean Lee, Ning Li, Bing-Nan Lu, Ulf-G. Meiner, Gautam Rupak, Shihang Shen, Young-Ho Song and Gianluca Stellin, 15 May 2024, Nature. DOI: 10.1038/s41586-024-07422-z

The first author is Prof. Dr. Serdar Elhatisari, who worked for two years as a Fellow in Prof. Meiners ERC Advanced Grant EXOTIC. According to Meiner, a large part of the work was carried out during this time. Part of the computing time on supercomputers at Forschungszentrum Jlich was provided by the IAS-4 institute, which Meiner heads.

The first author, Prof. Dr. Serdar Elhatisari, comes from the University of Bonn and Gaziantep Islam Science and Technology University (Turkey). Significant contributions were also made at Michigan State University. Other participants include Ruhr University Bochum, South China Normal University (China), the Institute for Basic Science in Daejeon (South Korea), Sun Yat-Sen University in Guangzhou (China), the Graduate School of China Academy of Engineering Physics in Beijing (China), Mississippi State University (USA) and Universit Paris-Saclay (France). The study was funded by the U.S. Department of Energy, the U.S. National Science Foundation, the German Research Foundation, the National Natural Science Foundation of China, the Chinese Academy of Sciences Presidents International Fellowship Initiative, the Volkswagen Foundation, the European Research Council, the Scientific and Technological Research Council of Turkey, the National Security Academic Fund, the Rare Isotope Science Project of the Institute for Basic Science, the National Research Foundation of Korea, the Institute for Basic Science and the Espace de Structure et de reactions Nucleaires Theorique.

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Unlocking the Quantum Code: International Team Cracks a Long-Standing Physics Problem - SciTechDaily

Patrik Schach and Enno Giese, physicists at TU Darmstadt, are looking to redefine timethey believe our previous measurements may have been inaccurate. The researchers have arrived at this proposal thanks to the phenomenon of quantum tunneling, where particles appear to move faster than the speed of light.

We make sense of the world around us with classical mechanics. In this realm, the laws of physics reign supreme, and particles tend to follow them. Dig a bit deeper into the quantum realm, though, and even the theory of relativity comes crashing down.

The faster-than-light travel of particles inside a quantum tunnel has prompted researchers to question whether we have accurately measured time. Schach and Giese have proposed a new experimental design to measure time for a tunneling particle, considering its unique abilities in the quantum realm.

In classical physics, a particle such as an electron can only pass through a potential energy barrier if it has the energy to overcome it. On the other hand, in quantum mechanics, the particle can cross over such a barrier even if its energy levels are lower. This is referred to as quantum tunneling.

This is attributed to the particles wave-like properties in quantum mechanics, which allow it to tunnel through the barrier even at a lower energy level. According to quantum mechanics, this tunneling is subjective to the width and height of the barrier and the particles energy.

Even though tunneling also seems to break the laws of energy conservation, the particle appears on the other side of the barrier with the same energy as before. So, no energy is gained or lost during the process.

Researchers believe that tunneling also plays a role in radioactive decay, allowing particles to escape the nucleus even though they do not have sufficient energy to escape the nuclear potential barrier. Additionally, the phenomenon could help serve applications such as microscopy and memory storage.

According to quantum mechanics, atoms can behave like waves and particles simultaneously. Their wave nature can help them overcome an energy barrier. However, when atoms are tunneling, it becomes difficult to predict when they will appear on the other side, i.e., when they need to tunnel.

Instead of relying on conventional approaches to measure time, Schach and Giese propose using the tunneling particle as a clock. A non-tunneling particle will serve as a reference in such a setup.

By comparing these two natural clocks, the researchers aim to determine whether time travels faster, slower, or equally fast when the particle is tunneling.

The researchers plan to use the oscillating energy levels between atoms to achieve this. Using a laser pulse, the researchers will oscillate the atoms and start the clock. During tunneling, a small shift in the rhythm occurs, and a second laser pulse will be used to cause the waves to interfere.

By measuring the interference, the team can precisely measure the elapsed time. The challenge, however, is that the time difference to be measured is extremely short, 10-26 seconds. To overcome this, the researchers propose using clouds of atoms instead of individual atoms to amplify the effect.

The experimental design has been published in the journal Science Advances.

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Ameya Paleja Ameya is a science writer based in Hyderabad, India. A Molecular Biologist at heart, he traded the micropipette to write about science during the pandemic and does not want to go back. He likes to write about genetics, microbes, technology, and public policy.

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Quantum tunnel: Scientists study particles that move faster than light - Interesting Engineering

It can be hard to wrap our minds round the very large and the very small. Ron Koeberer/Millennium Images, UK

Imagine setting off on a spacecraft that can travel at the speed of light. You wont get far. Even making it to the other side of the Milky Way would take 100,000 years. It is another 2.5 million years to Andromeda, our nearest galactic neighbour. And there are some 2 trillion galaxies beyond that.

The vastness of the cosmos defies comprehension. And yet, at the fundamental level, it is made of tiny particles.It is a bit of a foreign country both the small and the very big, says particle physicist Alan Barr at the University of Oxford. I dont think you ever really understand it, you just get used to it.

Still, you need to have some grasp of scale to have any chance of appreciating how reality works.

Lets start big, with the cosmic microwave background (CMB), the radiation released 380,000 years after the big bang. The biggest scales weve measured are features in the CMB, says astrophysicist Pedro Ferreira, also at the University of Oxford. These helped us put the diameter of the observable universe at 93 billion light years.

At the other end of the scale, the smallest entities are fundamental particles like quarks. Yet quantum physics paints these as dimensionless blips in a quantum field, with no size at all. So what is the shortest possible distance? The best we can do is the so-called Planck length, which is about

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Quantum to cosmos: Why scale is vital to our understanding of reality - New Scientist

A variation on the theory of quantum gravity the unification of quantum mechanics and Einstein's general relativity could help solve one of the biggest puzzles in cosmology, new research suggests.

For nearly a century, scientists have known that the universe is expanding. But in recent decades, physicists have found that different types of measurements of the expansion rate called the Hubble parameter produce puzzling inconsistencies.

To resolve this paradox, a new study suggests incorporating quantum effects into one prominent theory used to determine the expansion rate.

"We tried to resolve and explain the mismatch between the values of the Hubble parameter from two different prominent types of observations," study co-author P.K. Suresh, a professor of physics at the University of Hyderabad in India, told Live Science via email.

The universe's expansion was first identified by Edwin Hubble in 1929. His observations with the largest telescope of that time revealed that galaxies farther from us appear to move away at faster speeds. Although Hubble initially overestimated the expansion rate, subsequent measurements have refined our understanding, establishing the current Hubble parameter as highly reliable.

Later in the 20th century, astrophysicists introduced a novel technique to gauge the expansion rate by examining the cosmic microwave background, the pervasive "afterglow" of the Big Bang.

However, a serious problem arose with these two types of measurements. Specifically, the newer method produced a Hubble parameter value almost 10% lower than the one deduced from the astronomical observations of distant cosmic objects. Such discrepancies between different measurements, called the Hubble tension, signal potential flaws in our understanding of the universe's evolution.

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Related: Newfound 'glitch' in Einstein's relativity could rewrite the rules of the universe, study suggests

In a study published in the journal Classical and Quantum Gravity, Suresh and his colleague from the University of Hyderabad, B. Anupama, proposed a solution to align these disparate results. They underscored that physicists infer the Hubble parameter indirectly, employing our universe's evolutionary model based on Einstein's theory of general relativity.

The team argued for revising this theory to incorporate quantum effects. These effects, intrinsic to fundamental interactions, encompass random field fluctuations and the spontaneous creation of particles from the vacuum of space.

Despite scientists' ability to integrate quantum effects into theories of other fields, quantum gravity remains elusive, making detailed calculations extremely difficult or even impossible. To make matters worse, experimental studies of these effects require reaching temperatures or energies many orders of magnitude higher than those achievable in a lab.

Acknowledging these challenges, Suresh and Anupama focused on broad quantum-gravity effects common to many proposed theories.

"Our equation doesn't need to account for everything, but that does not prevent us from testing quantum gravity or its effects experimentally," Suresh said.

Their theoretical exploration revealed that accounting for quantum effects when describing the gravitational interactions in the earliest stage of the universe's expansion, called cosmic inflation, could indeed alter the theory's predictions regarding the properties of the microwave background at present, making the two types of Hubble parameter measurements consistent.

Of course, final conclusions can be drawn only when a full-fledged theory of quantum gravity is known, but even the preliminary findings are encouraging. Moreover, the link between the cosmic microwave background and quantum gravitational effects opens the way to experimentally studying these effects in the near future, the team said.

"Quantum gravity is supposed to play a role in the dynamics of the early universe; thus its effect can be observed through measurements of the properties of the cosmic microwave background," Suresh said.

"Some of the future missions devoted to studying this electromagnetic background are highly probable and promising to test quantum gravity. It provides a promising suggestion to resolve and validate the inflationary models of cosmology in conjunction with quantum gravity."

Additionally, the authors posit that quantum gravitational phenomena in the early universe might have shaped the properties of gravitational waves emitted during that period. Detecting these waves with future gravitational-wave observatories could further illuminate quantum gravitational characteristics.

"Gravitational waves from various astrophysical sources have only been observed so far, but gravitational waves from the early universe have not yet been detected," Suresh said. "Hopefully, our work will help in identifying the correct inflationary model and detecting the primordial gravitational waves with quantum gravity features."

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A new theory of quantum gravity could explain the biggest puzzle in cosmology, study suggests - Livescience.com

As part of theCenter for Quantum Leaps, a signature initiative of the Arts & Sciences strategic plan, physicistKater Murchand his research group use nano-fabrication techniques toconstruct superconducting quantum circuitsthat allow them to probe fundamental questions in quantum mechanics. Qubits are promising systems for realizing quantum schemes for computation, simulation and data encryption.

Murch and his collaborators published a new paper inPhysical Review Lettersthat explores the effects of memory in quantum systems and ultimately offers a novel solution to decoherence, one of the primary problems facing quantum technologies.

Our work shows that theres a new way to prevent decoherence from corrupting quantum entanglement, said Murch, the Charles M. Hohenberg Professor of Physics at Washington University in St. Louis. We can use dissipation to prevent entanglement from leaving our qubits in the first place.

View the teams illustrated video about their research findings:https://youtu.be/EbeNagXqJEk

Learn more about WashUs quantum research in theAmpersandmagazine.

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Helping qubits stay in sync - Newswise

Quantum tunneling allows particles to bypass energy barriers. A new method has been proposed to measure the time it takes for particles to tunnel, which could challenge previous assertions of superluminal tunneling speeds. This method involves using atoms as clocks to detect subtle time differences. Credit: SciTechDaily.com

In an amazing phenomenon of quantum physics known as tunneling, particles appear to move faster than the speed of light. However, physicists from Darmstadt believe that the time it takes for particles to tunnel has been measured incorrectly until now. They propose a new method to stop the speed of quantum particles.

In classical physics, there are strict laws that cannot be circumvented. For instance, if a rolling ball lacks sufficient energy, it will not get over a hill; instead, it will roll back down before reaching the peak. In quantum physics, this principle is not quite so strict. Here, a particle may pass a barrier, even if it does not have enough energy to go over it. It acts as if it is slipping through a tunnel, which is why the phenomenon is also known as quantum tunneling. Far from mere theoretical magic, this phenomenon has practical applications, such as in the operation of flash memory drives.

In the past, experiments in which particles tunneled faster than light drew some attention. After all, Einsteins theory of relativity prohibits faster-than-light velocities. The question is therefore whether the time required for tunneling was stopped correctly in these experiments. Physicists Patrik Schach and Enno Giese from TU Darmstadt follow a new approach to define time for a tunneling particle. They have now proposed a new method of measuring this time. In their experiment, they measure it in a way that they believe is better suited to the quantum nature of tunneling. They have published the design of their experiment in the renowned journal Science Advances.

According to quantum physics, small particles such as atoms or light particles have a dual nature.

Depending on the experiment, they behave like particles or like waves. Quantum tunneling highlights the wave nature of particles. A wave packet rolls towards the barrier, comparable to a surge of water. The height of the wave indicates the probability with which the particle would materialize at this location if its position were measured. If the wave packet hits an energy barrier, part of it is reflected. However, a small portion penetrates the barrier and there is a small probability that the particle will appear on the other side of the barrier.

Previous experiments observed that a light particle has traveled a longer distance after tunneling than one that had a free path. It would therefore have traveled faster than the light. However, the researchers had to define the location of the particle after its passage. They chose the highest point of its wave packet.

But the particle does not follow a path in the classical sense, objects Enno Giese. It is impossible to say exactly where the particle is at a particular time. This makes it difficult to make statements about the time required to get from A to B.

Schach and Giese, on the other hand, are guided by a quote from Albert Einstein: Time is what you read off a clock. They suggest using the tunneling particle itself as a clock. A second particle that does not tunnel serves as a reference. By comparing these two natural clocks, it is possible to determine whether time elapses slower, faster or equally fast during quantum tunneling.

The wave nature of particles facilitates this approach. The oscillation of waves is similar to the oscillation of a clock. Specifically, Schach and Giese propose using atoms as clocks. The energy levels of atoms oscillate at certain frequencies. After addressing an atom with a laser pulse, its levels initially oscillate synchronized the atomic clock is started. During tunneling, however, the rhythm shifts slightly. A second laser pulse causes the two internal waves of the atom to interfere. Detecting the interference makes it possible to measure how far apart the two waves of the energy levels are, which in turn is a precise measure of the elapsed time.

A second atom, which does not tunnel, serves as a reference to measure the time difference between tunneling and non-tunneling. Calculations by the two physicists suggest that the tunneling particle will show a slightly delayed time. The clock that is tunneled is slightly older than the other, says Patrik Schach. This seems to contradict experiments that attributed superluminal speed to tunneling.

In principle, the test can be carried out with todays technology, says Schach, but it is a major challenge for experimenters. This is because the time difference to be measured is only around 10-26 seconds an extremely short time. It helps to use clouds of atoms as clocks instead of individual atoms, explains the physicist. It is also possible to amplify the effect, for example by artificially increasing the clock frequencies.

We are currently discussing this idea with experimental colleagues and are in contact with our project partners, adds Giese. It is quite possible that a team will soon decide to carry out this exciting experiment.

Reference: A unified theory of tunneling times promoted by Ramsey clocks by Patrik Schach and Enno Giese, 19 April 2024,Science Advances. DOI: 10.1126/sciadv.adl6078

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Breaking Light Speed: The Quantum Tunneling Enigma - SciTechDaily

In the fascinating realm of quantum physics, particles seem to defy the laws of classical mechanics, exhibiting mind-bending phenomena that challenge our understanding of the universe. One such phenomenon is quantum tunneling.

In quantum tunnels, particles appear to move faster than the speed of light, seemingly breaking the fundamental rules set by Einsteins theory of relativity.

However, a group of physicists from TU Darmstadt has proposed a new method to measure the time it takes for particles to tunnel, suggesting that previous experiments may have been inaccurate.

Patrik Schach and Enno Giese, physicists from TU Darmstadt, have published their groundbreaking experiment design in the prestigious journal Science Advances.

Their approach aims to redefine the concept of time for a tunneling particle, taking into account the quantum nature of the phenomenon.

Quantum tunneling is a phenomenon in quantum mechanics where a particle, such as an electron, passes through a potential energy barrier that it classically cannot surmount.

In classical physics, if a particle doesnt have enough energy to overcome a barrier, it will simply bounce back or stop.

However, in quantum mechanics, particles exhibit wave-like properties, and there is a probability that the particle can tunnel through the barrier, even if it lacks the energy to cross it classically.

Here are some key points to understand about quantum tunnels:

Particles in quantum mechanics possess both wave and particle properties. The wave nature of particles allows them to exhibit behaviors that are not possible in classical physics.

The probability of a particle tunneling through a barrier depends on factors such as the barriers width and height, and the particles energy.

Quantum tunneling does not violate the law of energy conservation. The particle does not gain or lose energy while tunneling. Instead, it appears on the other side of the barrier with the same energy it had before.

Quantum tunneling has numerous practical applications, including scanning tunneling microscopy (STM), which allows scientists to image surfaces at the atomic level, and flash memory drives that use quantum tunneling to store and access data.

Quantum tunneling also plays a role in radioactive decay, where particles escape the nucleus of an atom despite not having enough energy to overcome the nuclear potential barrier.

According to quantum physics, small particles such as atoms or light particles possess a dual nature, behaving like both particles and waves depending on the experiment.

As mentioned previously, quantum tunneling highlights the wave nature of particles, where a wave packet rolls towards an energy barrier, and a small portion of it penetrates the barrier, resulting in a probability that the particle will appear on the other side.

But the particle does not follow a path in the classical sense, objects Enno Giese. It is impossible to say exactly where the particle is at a particular time. This makes it difficult to make statements about the time required to get from A to B.

Inspired by Albert Einsteins quote, Time is what you read off a clock, Schach and Giese propose using the tunneling particle itself as a clock, with a second non-tunneling particle serving as a reference.

By comparing these two natural clocks, they aim to determine whether time elapses slower, faster, or equally fast during quantum tunneling.

The researchers suggest using atoms as clocks, taking advantage of the oscillating energy levels within them. By addressing an atom with a laser pulse, its levels initially oscillate in sync, starting the atomic clock.

During tunneling, the rhythm shifts slightly, and a second laser pulse causes the two internal waves of the atom to interfere. Detecting this interference allows for precise measurement of the elapsed time.

The clock that is tunneled is slightly older than the other, says Patrik Schach, contradicting experiments that attributed superluminal speed to tunneling.

While the proposed experiment can be carried out with todays technology, it presents a significant challenge for experimenters. The time difference to be measured is extremely short, around 10-26 seconds.

To overcome this, the researchers suggest using clouds of atoms as clocks instead of individual atoms and amplifying the effect by artificially increasing the clock frequencies.

We are currently discussing this idea with experimental colleagues and are in contact with our project partners, adds Giese. The possibility of a team deciding to carry out this exciting experiment in the near future is quite real.

In summary, Patrik Schach and Enno Gieses experiment design challenges our understanding of time and particle behavior in the quantum realm.

By proposing a new method to measure the time it takes for particles to tunnel, they are questioning previous assumptions about superluminal speeds and presenting new avenues for exploring the mysteries of quantum physics.

As they collaborate with experimental colleagues and project partners, the possibility of conducting this exciting experiment draws closer, promising to unlock the secrets of the quantum universe and pave the way for a deeper understanding of the fundamental nature of reality.

The full study was published in the journal Science Advances.

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Quantum tunnels allow particles to break the light-speed barrier - Earth.com

Phase-controlled projection measurement of quantum erasers for superresolution

Figure1 shows a universal scheme of the classically (coherently) excited superresolution based on phase-controlled quantum erasers. The superresolution scheme in Fig.1 originates in the Nth-order intensity correlations between phase-controlled quantum erasers, resulting in the PBW-like quantum feature11,25, as shown in Fig.2. Compared to the N=4 case11,25, the Inset of Fig.1 shows an arbitrary Nth-order superresolution scheme, where the first eight quantum erasers for N=8 are visualized with dotted blocks to explain the cascaded phase control of the quantum erasers using QWPs. For the quantum eraser, both single photon8 and cw laser light9 were experimentally demonstrated in a MachZehnder interferometer (MZI) for the polarization-basis projection onto a polarizer P. The MZI physics of coherence optics37 shows the same feature in both a single photon15 and cw light due to the limited Sorkin parameter, as discussed for the Born rule tests38. This originates in the equality between quantum and classical approaches for the first-order (N=1) intensity correlation24. Quantum mechanically, the deterministic feature of the MZI system is due to the double unitary transformation of a 50/50 nonpolarizing beam splitter (BS)1,15. The use of neutral density filters is not to generate single photons but to protect photodiodes from intensity saturation.

Schematic of a universal super-resolution based on phase-controlled quantum erasers. L: laser, ND: neutral density filter, H: half-wave plate, PBS: polarizing beam splitter, PZT: piezo-electric transducer, QWP: quarter-wave plate, P: polarizer, D: single photon (or photo-) detector, All rotation angles of Ps are at (uptheta =45^circ).

Numerical calculations of the Nth order intensity correlations in Fig.1. (upperleft) Individual first-order intensity correlation ({I}_{j}) in A, B, C, and D blocks. Blue star (circle): B3 (B4) in B, Cyan star (circle): C3 (C4) in C, Red star (circle): A3 (A4) in A, Magenta star (circle): D3 (D4) in D. (upper right) Second-order intensity correlation in each block of the Inset of Fig. 1.(lower right) Fourth-order intensity correlation between (red) A and B, and (blue) C and D. (lowerleft) Eight-order intensity product between all quantum erasers. ({I}_{K}={I}_{K1}{I}_{K2}) (K=A, B, C, D), ({I}_{AB}^{(4)}={I}_{A}^{(2)}{I}_{B}^{(2)}), ({I}_{CD}^{(4)}={I}_{C}^{(2)}{I}_{D}^{(2)}), and ({I}_{ABCD}^{(8)}={I}_{AB}^{(4)}{I}_{CD}^{(4)}). ({xi }_{A}=frac{pi }{2}), ({xi }_{C}=frac{pi }{4}), and ({xi }_{D}=frac{3pi }{4}).

The rotation angle of QWP in each block of the quantum erasers in the Inset of Fig.1 is to induce a phase gains (({xi }_{j})) to the vertical component of the corresponding light37. As experimentally demonstrated25, the QWP induces a phase delay to the vertical polarization component compared to the horizontal one37. This polarization-basis-dependent phase gain of the light directly affects the quantum eraser via polarization-basis projection measurements, resulting in a fringe shift11,25, because the role of the polarizer P is to project orthogonal polarization bases onto the common axis (widehat{{text{p}}}) (see Eqs. (2)(8))8,9,18. The random path length to the polarizer from PBS in Fig.1 does not influence the intensity correlations due to the unaffected global phase by the Born rule, where intensity (measurement) is the absolute square of the amplitude13,14. Thus, controlling the QWP of each block makes an appropriate fringe shift of the quantum erasers for the first-order intensity products.

In the proposed universal scheme with a practically infinite number of phase-controlled quantum erasers in Fig.1, a general coherence solution of the phase-controlled superresolution is coherently derived from the combinations of QWPs (see Eq.(25) and Figs. 2 and 3). Then, the general solution is compared with PBWs based on N00N states for the discussion of phase quantization of the Nth-order intensity product in Fig.4. Such phase quantization has already been separately discussed for coherence de Broglie waves (CBWs) in a coupled MZI system for the wave nature of quantum mechanics39,40. Unlike CBWs resulting from MZI superposition, the present phase quantization of superresolution is for the intensity product between phase-controlled quantum erasers. On the contrary to energy quantization of the particle nature in quantum mechanics1, the phase quantization is for the wave nature, where the particle and wave natures are mutually exclusive.

Numerical calculations for the normalized Kth-order intensity products. K represents the number of quantum erasers used for intensity product measurements.

Phase quantization of the intensity products in Fig.3. K is the order of intensity product. Dotted: K=1, Cyan: K=2, Blue: K=4, Red: K=8.

A coherence approach based on the wave nature of a photon is adopted to analyze Fig.1 differently from the quantum approach based on quantum operators1,26,27,28,29,30,31,32,33. The novel feature of the present method is to use common intensity products of cw lights via polarization-basis projection of the phase-controlled quantum erasers. Thus, there is no need for single-photon coincidence detection. Instead, the intensity product is enough for a single shot measurement, as is in nonlinear optics. Technically, the condition ({text{N}}le {text{M}}) is required, where N and M are the number of quantum erasers used for the intensity product and the photon number of the input light, respectively. Here it should be noted that both intensity product and coincidence detection are effective within the ensemble coherence time of the input light L. In that sense, a pulsed laser is more appropriate for the use of a time-bin scheme as shown for quantum key distribution41.

The amplitude of the output field of the Michelson interferometer in Fig.1 is represented using the BS matrix representation42as:

$${{varvec{E}}}_{A}=frac{i{E}_{0}}{sqrt{2}}left(widehat{H}{e}^{ivarphi }+widehat{V}right)$$

(1)

where ({E}_{0}) is the amplitude of the light just before entering the Michelson interferometer. (widehat{H}) and (widehat{V}) are unit vectors of horizontal and vertical polarization bases of the light, respectively. In Eq.(1), the original polarization bases are swapped by the 45 rotated QWPs inserted in both paths for full throughput to the ({E}_{A}) direction. Due to the orthogonal bases, Eq.(1) results in no fringe, satisfying the distinguishable photon characteristics of the particle nature in quantum mechanics: (langle {I}_{A}rangle ={I}_{0}).

By the rotated polarizers in Fig.1, whose rotation angle (uptheta) is from the horizontal axis, Eq.(1) is modified for the split quantum erasers:

$${{varvec{E}}}_{A1}=frac{i{E}_{0}}{sqrt{2}sqrt{8}}left(costheta {e}^{ivarphi }+sintheta {e}^{i{xi }_{A}}right)widehat{p}$$

(2)

$${{varvec{E}}}_{A2}=frac{-{E}_{0}}{sqrt{2}sqrt{8}}left(-costheta {e}^{ivarphi }+sintheta {e}^{i{xi }_{A}}right)widehat{p}$$

(3)

$${{varvec{E}}}_{B1}=frac{-i{E}_{0}}{sqrt{2}sqrt{8}}left(costheta {e}^{ivarphi }+sintheta right)widehat{p}$$

(4)

$${{varvec{E}}}_{B2}=frac{-i{E}_{0}}{sqrt{2}sqrt{8}}left(-costheta {e}^{ivarphi }+sintheta right)widehat{p}$$

(5)

$${{varvec{E}}}_{C1}=frac{-{E}_{0}}{sqrt{2}sqrt{8}}left(costheta {e}^{ivarphi }+sintheta {e}^{i{xi }_{C}}right)widehat{p}$$

(6)

$${{varvec{E}}}_{C2}=frac{-i{E}_{0}}{sqrt{2}sqrt{8}}left(-costheta {e}^{ivarphi }+sintheta {e}^{i{xi }_{C}}right)widehat{p}$$

(7)

$${{varvec{E}}}_{D1}=frac{-i{E}_{0}}{sqrt{2}sqrt{8}}left(costheta {e}^{ivarphi }+sintheta {e}^{i{xi }_{D}}right)widehat{p}$$

(8)

$${{varvec{E}}}_{D2}=frac{{E}_{0}}{sqrt{2}sqrt{8}}left(-costheta {e}^{ivarphi }+sintheta {e}^{i{xi }_{D}}right)widehat{p}$$

(9)

where (widehat{p}) is the axis of the polarizers, and (sqrt{8}) is due to the eight divisions (N=8) of ({{varvec{E}}}_{A}) by the lossless BSs. In Eqs. (2)(9), the projection onto the polarizer results in (widehat{H}to costheta widehat{p}) and (widehat{V}to sintheta widehat{p}). By BS, the polarization direction of (widehat{H}) is reversed, as shown in the mirror image37. By the inserted QWP in each block, the ({xi }_{j})-dependent phase gain is to the (widehat{V}) component only37. As demonstrated for the projection measurement of N interfering entangled photons23,29, the Nth-order intensity correlation is conducted by the N split ports in the Inset of Fig.1.

Thus, the corresponding mean intensities of all QWP-controlled quantum erasers in the Inset of Fig.1 are as follows for (uptheta =45^circ) of all Ps:

$$langle {I}_{A1}rangle =frac{{I}_{0}}{2N}langle 1+{{cos}}(varphi -{xi }_{A})rangle$$

(10)

$$langle {I}_{A2}rangle =frac{{I}_{0}}{2N}langle 1-{{cos}}(varphi -{xi }_{A})rangle$$

(11)

$$langle {I}_{B1}rangle =frac{{I}_{0}}{2N}langle 1+cosvarphi rangle$$

(12)

$$langle {I}_{B2}rangle =frac{{I}_{0}}{2N}langle 1-cosvarphi rangle$$

(13)

$$langle {I}_{C1}rangle =frac{{I}_{0}}{2N}leftlangle 1+{cos}(varphi -{xi }_{C})rightrangle$$

(14)

$$langle {I}_{C2}rangle =frac{{I}_{0}}{2N}leftlangle 1-{cos}(varphi -{xi }_{C})rightrangle$$

(15)

$$langle {I}_{D1}rangle =frac{{I}_{0}}{2N}leftlangle 1+{cos}(varphi -{xi }_{D})rightrangle$$

(16)

$$langle {I}_{D2}rangle =frac{{I}_{0}}{2N}leftlangle 1-{cos}(varphi -{xi }_{D})rightrangle$$

(17)

Equations(10)(17) are the unveiled quantum mystery of the cause-effect relation of the quantum eraser found in the ad-hoc polarization-basis superposition via the polarization projection onto the (widehat{p}) axis of the polarizer. The price to pay for this quantum mystery is 50% photon loss by the polarization projection11,22, regardless of single photons8 or cw light9. By adjusting ({xi }_{j}) of QWP in each block, appropriate fringe shifts of the quantum erasers can also be made accordingly, as shown in Fig.2 for ({xi }_{A}=frac{pi }{2}), ({xi }_{C}=frac{pi }{4}), and ({xi }_{D}=frac{3pi }{4}).

The corresponding second-order (N=2) intensity correlations between the quantum erasers in each block is directly obtained from Eqs. (10)(17) for ({xi }_{A}=frac{pi }{2}), ({xi }_{C}=frac{pi }{4}), and ({xi }_{D}=frac{3pi }{4}):

$$leftlangle {{text{I}}}_{A1A2}^{(2)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{2}leftlangle {sin}^{2}left(varphi -frac{pi }{2}right)rightrangle$$

(18)

$$leftlangle {{text{I}}}_{B1B2}^{(2)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{2}leftlangle {sin}^{2}varphi rightrangle$$

(19)

$$leftlangle {{text{I}}}_{C1C2}^{(2)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{2}leftlangle {sin}^{2}left(varphi -frac{pi }{4}right)rightrangle$$

(20)

$$leftlangle {{text{I}}}_{D1D2}^{(2)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{2}leftlangle {sin}^{2}left(varphi -frac{3pi }{4}right)rightrangle$$

(21)

where the second-order intensity fringes are also equally shifted as in the first-order fringes (see Fig.2). Likewise, the fourth-order (N=4) intensity correlations between any two blocks can be derived from Eqs. (18)(21) as:

$$leftlangle {{text{I}}}_{A1A2B1B2}^{(4)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{4}leftlangle {sin}^{2}varphi {sin}^{2}left(varphi -frac{pi }{2}right)rightrangle$$

(22)

$$leftlangle {{text{I}}}_{C1C2D1D2}^{(4)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{4}leftlangle {sin}^{2}left(varphi -frac{pi }{4}right){sin}^{2}left(varphi -frac{3pi }{4}right)rightrangle$$

(23)

Thus, the eighth-order (N=8) intensity correlation for all quantum erasers in the Inset of Fig.1 is represented as:

$$leftlangle {{text{I}}}_{A1A2B1B2C1C2D1D2}^{(8)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{8}leftlangle {sin}^{2}varphi {sin}^{2}left(varphi -frac{pi }{4}right){sin}^{2}left(varphi -frac{pi }{2}right){sin}^{2}left(varphi -frac{3pi }{4}right)rightrangle$$

(24)

From Eq.(24), the proposed scheme of superresolution for N=8 is analytically confirmed for the satisfaction of the Heisenberg limit in quantum sensing (see Figs. 2 and 3).

Figure2 shows numerical calculations of the Nth-order intensity correlations using Eqs. (10)(17) for ({xi }_{A}=uppi /2), ({xi }_{C}=uppi /4), and ({xi }_{D}=3uppi /4) to demonstrate the proposed PBW-like superresolution using phase-controlled coherent light in Fig.1. From the upper-left panel to the clockwise direction in Fig.2, the simulation results are shown for ordered (N=1, 2, 4, 8) intensity correlations. As shown, all ordered-intensity correlations are equally spaced in the phase domain, where the pair of quantum erasers in each block satisfies the out-of-phase relation (see the same colored o and * curves in the upper-left panel). Thus, the higher-order intensity correlation between blocks also results in the same out-of-phase relation, as shown for N=2 and N=4, resulting in the Heisenberg limit, (mathrm{delta varphi }=uppi /{text{N}}).

For an arbitrary order N, the jth block with ({xi }_{j})-QWP can be assigned to the universal scheme of the phase-controlled superresolution. For the expandable finite block series with ({xi }_{j})-phase-controlled quantum erasers in Fig.1, the generalized solution of the kth-order intensity correlation can be quickly deduced from Eq.(24):

$$leftlangle {{text{I}}}^{(K)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{K}leftlangle prod_{j=0}^{K}{sin}^{2}(varphi -{xi }_{j})rightrangle$$

(25)

where ({xi }_{j}=j2pi /N) and ({text{K}}le {text{N}}). Unlike the N00N-based superresolution in quantum sensing26,27,28,29,30,31, the kth-order intensity product in Eq.(25) can be coherently amplified as usual in classical (coherence) sensors. Thus, the reduction by ({left(frac{{I}_{0}}{2N}right)}^{k}) has no critical problem for potential applications of the proposed superresolution.

Figure3 is for the details of numerical calculations for K=1,2,...,8 and K=80 using Eq.(25). The top panels of Fig.3 are for odd and even Ks, where the fringe number linearly increases as K increases, satisfying the Heisenberg limit31. For the K-proportional fringe numbers, the positions of the first fringes for K=1,2,...,8 move from (uppi /2) for K=1 (black dot, left panel) to (uppi /16) for K=8 (blue dot, middle panel). As in PBWs, thus, the same interpretation of the K-times increased effective frequency to the original frequency of the input light can be made for the Kth-order intensity correlations. Unlike N00N state-based PBWs, the intensity-product order can be post-determined by choosing K detectors out of N quantum erasers.

The right panel of Fig.3 is for comparison purposes between K=8 and K=80, where the resulting ten times increased fringe numbers indicate ten times enhanced phase resolution, satisfying the Heisenberg limit. Thus, the pure coherence solution of the PBW-like quantum feature satisfying the Heisenberg limit is numerically confirmed for the generalized solution of Eq.(25). Here, the coincidence detection in the particle nature of quantum sensing with N00N states is equivalent to the coherence intensity-product measurement, where the coherence between quantum erasers is provided by the cw laser L within its spectral bandwidth. Furthermore, the ({xi }_{j}) relation between blocks composed of paired quantum erasers may imply the phase relation between paired entangled photons (discussed elsewhere).

Figure4 discusses the perspective of the phase-basis relation provided by ({xi }_{j}) in Eq.(25) for the Kth-order intensity correlations of the proposed superresolution. From the colored dots representing the first fringes of the ordered intensity products, the generalized phase basis of the Kth-order intensity correlation can be deduced for ({mathrm{varphi }}_{K}=uppi /{text{K}}). Thus, the Kth-order intensity correlation behaves as a K-times increased frequency ({f}_{K} (=K{f}_{0})) to the original input frequency ({f}_{0}) of L. The intensity-order dependent effective frequency ({f}_{K}) is equivalent to the PBW of the N00N state in quantum metrology26,27,28,29,30,31,32.

Based on the K-times increased fringes in the Kth-order intensity product, the numerical simulations conducted in Fig.4 can be interpreted as phase quantization of the intensity products through projection measurements of the quantum erasers. As shown in the PBW-like quantum features, these discrete eigenbases of the intensity products can also be compared to a K-coupled pendulum system43, where the phase quantization in Fig.4 can be classically understood39,40. Unlike the N-coupled pendulum system43 or CBWs from MZI interference39,40, however, any specific mode of ({varphi }_{K}) can be deterministically taken out by post-selection of a particular number of blocks used for the intensity-product order K in Fig.1. Like the energy quantization of the particle nature in quantum mechanics, thus, Fig.4 is another viewpoint of the wave nature for the proposed superresolution. By the wave-particle duality in quantum mechanics, both features of the energy and phase quantization are mutually exclusive.

From the universal scheme of the superresolution based on the phase-controlled quantum erasers in Fig.1, a generalized solution of the Kth-order intensity correlation in Fig.4 can also be intuitively obtained:

$$leftlangle {{text{I}}}_{{P}_{1}{P}_{2}dots {P}_{j}dots {P}_{K/2}}^{(K)}(0)rightrangle ={left(frac{{I}_{0}}{2N}right)}^{K}leftlangle {sin}^{2}(Kvarphi /2)rightrangle$$

(26)

where ({P}_{j}={Z}_{1}{Z}_{2}), and ({Z}_{j}) is the jth quantum eraser of the P block. Here, the effective phase term (Kvarphi) in Eq.(26) represents the typical nonclassical feature of PBWs used for quantum sensing with N00N states 30,31. The numerical simulations of Eq.(26) for N=1, 2, 4, and 8 perfectly match those in Fig.4 (not shown). Although the mathematical forms between Eqs. (25) and (26) are completely different, their quantum behaviors are the same as each other. Thus, Eq.(26) is equivalent to the superresolution in Eq.(25) 13,25, where the phase quantization is accomplished by ordered intensity products of the divided output fields of the Michelson interferometer. Unlike coincidence detection between entangled photons under the particle nature26,27,28,29,30,31,32, the present coherence scheme with the wave nature is intrinsically deterministic within the spectral bandwidth of the input laser. Thus, the coincidence detection in N00N-based quantum sensing is now replaced by the intensity product between independently phase-controlled quantum erasers using QWPs. Such a coherence technique of the individually and independently controlled quantum erasers can be applied for a time-bin scheme with a pulsed laser, where intensity products between different time bins are completely ignored due to their incoherence feature41.

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