Periodic Reporting for period 2 - EnHydro (Entanglement measures in pilot-wave hydrodynamics)
Reporting period: 2021-07-01 to 2022-06-30
What is the problem/issue being addressed?
The project aims at finding laboratory-scale analogs of quantum phenomena, especially of the ones involving bipartite systems. The main project goal is to build quantum analogue by making use of fluid systems that are readily observed and studied in the laboratory due to their relevant scale (mm – cm). Even though quantum theory can be formulated in terms of wave mechanics, its similarities to the wave theory describing the fluid systems is not unlimited. One of the major issues when looking for quantum analogs, is to very well define both the potential and the limitations of each system, and this project contributes to that direction as well. Specifically, we do so by studying bipartite bouncing droplets systems that were not very well-understood prior to the project.
Why is it important for society?
One of the main puzzles in modern physics is that our two main theories, quantum mechanics and general relativity are not entirely compatible with each other. Specifically, general relativity is founded on the core assumption that no influence can travel faster than the speed of light in any reference frame, whereas in quantum entanglement, the measurement of one particle is assumed to affect the state of a distant particle instantaneously, a process known as the wave function collapse. This challenge is well-known and of great interest, both among scientists and the general public. This is a basic research project that, through the development of novel quantum analogs, aims to develop key ideas that will contribute in resolving this important challenge. As a basic research project we also aim to develop new visual tools of the hydrodynamic pilot-wave systems, which can be used to educate young students as to the open questions in quantum mechanics, and inspire them to think creatively.
What are the overall objectives?
The project aims to develop hydrodynamic analogs of key quantum phenomena involving bipartite systems, with particular interest in non-separability. Specifically, it aims to develop such analogs in 1D systems involving hydrodynamic cavities that interact through a common wavefield, and then to advance them in 2D systems, using the state-of-the-art experimental setup at MIT. In addition, it aims to rationalize the observed experimental behavior mathematically by developing appropriate numerical models, which in turn will improve our understanding of how such wave-mediated bipartite correlations are created in a pilot-wave system. These results will ultimately be compared with performed quantum mechanical experiments (from the literature) in different settings.
The project aims at finding laboratory-scale analogs of quantum phenomena, especially of the ones involving bipartite systems. The main project goal is to build quantum analogue by making use of fluid systems that are readily observed and studied in the laboratory due to their relevant scale (mm – cm). Even though quantum theory can be formulated in terms of wave mechanics, its similarities to the wave theory describing the fluid systems is not unlimited. One of the major issues when looking for quantum analogs, is to very well define both the potential and the limitations of each system, and this project contributes to that direction as well. Specifically, we do so by studying bipartite bouncing droplets systems that were not very well-understood prior to the project.
Why is it important for society?
One of the main puzzles in modern physics is that our two main theories, quantum mechanics and general relativity are not entirely compatible with each other. Specifically, general relativity is founded on the core assumption that no influence can travel faster than the speed of light in any reference frame, whereas in quantum entanglement, the measurement of one particle is assumed to affect the state of a distant particle instantaneously, a process known as the wave function collapse. This challenge is well-known and of great interest, both among scientists and the general public. This is a basic research project that, through the development of novel quantum analogs, aims to develop key ideas that will contribute in resolving this important challenge. As a basic research project we also aim to develop new visual tools of the hydrodynamic pilot-wave systems, which can be used to educate young students as to the open questions in quantum mechanics, and inspire them to think creatively.
What are the overall objectives?
The project aims to develop hydrodynamic analogs of key quantum phenomena involving bipartite systems, with particular interest in non-separability. Specifically, it aims to develop such analogs in 1D systems involving hydrodynamic cavities that interact through a common wavefield, and then to advance them in 2D systems, using the state-of-the-art experimental setup at MIT. In addition, it aims to rationalize the observed experimental behavior mathematically by developing appropriate numerical models, which in turn will improve our understanding of how such wave-mediated bipartite correlations are created in a pilot-wave system. These results will ultimately be compared with performed quantum mechanical experiments (from the literature) in different settings.
Bipartite correlations in the bouncing droplets pilot-wave hydrodynamic system have been investigated both numerically and experimentally. The first part of the study was numerical in 1D, where we have extended an existing model that was developed previously by A. Nachbin. Using this model, we were able to first create a 2-level system, comparable to an atomic two-level system, with well-defined ground and excited states. Using this, we were then able to demonstrate a hydrodynamic analog of quantum superradiance. Specifically, we have shown that the probability of a droplet to tunnel between its ground and excited states varies sinusoidally as a function of the separation distance between two two-level systems.
We then proceeded with an experimental demonstration of superradiance using interfacial fracture in 2D hydrodynamic cavities, whereby the droplet generation probability varies sinusoidally with distance. This further demonstrates that analogs of quantum superradiance, an otherwise purely quantum mechanical effect, can now be realized in two different hydrodynamic systems and by employing different physical mechanisms, thus strengthening our understanding of the analogy and its origins. Furthermore, this demonstrates the strength of the fluid mechanics systems in reproducing complex quantum processes in laboratory-scale experiments.
In the returning phase, we have devised a analogue of Bell inequalities using bouncing droplets. We introduce a new platform for addressing this question, a numerical model of coupled bipartite tunneling in the hydrodynamic pilot-wave system. We demonstrate that, under certain conditions, the Bell inequality is violated in a static Bell test owing to correlations induced by the wave-mediated coupling between the two subsystems. The platform will allow for further exploration of wave-mediated correlations in pilot-wave hydrodynamics, including more sophisticated Bell tests.
We then proceeded with an experimental demonstration of superradiance using interfacial fracture in 2D hydrodynamic cavities, whereby the droplet generation probability varies sinusoidally with distance. This further demonstrates that analogs of quantum superradiance, an otherwise purely quantum mechanical effect, can now be realized in two different hydrodynamic systems and by employing different physical mechanisms, thus strengthening our understanding of the analogy and its origins. Furthermore, this demonstrates the strength of the fluid mechanics systems in reproducing complex quantum processes in laboratory-scale experiments.
In the returning phase, we have devised a analogue of Bell inequalities using bouncing droplets. We introduce a new platform for addressing this question, a numerical model of coupled bipartite tunneling in the hydrodynamic pilot-wave system. We demonstrate that, under certain conditions, the Bell inequality is violated in a static Bell test owing to correlations induced by the wave-mediated coupling between the two subsystems. The platform will allow for further exploration of wave-mediated correlations in pilot-wave hydrodynamics, including more sophisticated Bell tests.
All results described in the previous section are beyond the state-of-the-art. We have two publication are available
1) V. Frumkin, J. W. M. Bush. K. Papatryfonos. Superradiant Droplet Emission from Parametrically Excited Cavities, Phys. Rev. Lett. 130, 064002 (2023)
2) K. Papatryfonos, M. Ruelle, C. Bourdiol, A. Nachbin, J.W.M. Bush, and M. Labousse. Hydrodynamic superradiance in wave-mediated cooperative tunneling, Communications Physics 5, 1, 142, (2022)
More recently, we showed that the static Bell inequality is violated by correlated droplets in certain geometries, where the geometry plays the role of the measurement setting in each side of the experiment. This is the first time that such inequalities are violated in a classical system that involves spatially-separated discrete particles, and a publication in currently under review to report these new results.
As a basic research project, we firstly aim to provide novel physical ideas that may advance our understanding of the laws of nature. Our long-term goal is that these ideas that we provide can also be tested by future large-scale quantum mechanical experiments that might modify our most fundamental theories in physics. By providing detailed analogs and explanations of how the correlations are developed in the fluidic systems, we aim to motivate such future investigations.Moreover by providing laboratory-scale analogs of complicated quantum phenomena that can be filmed using conventional cameras, we provide physical intuition of these phenomena, and thus a powerful educational and inspirational tool for young scientists and students.
1) V. Frumkin, J. W. M. Bush. K. Papatryfonos. Superradiant Droplet Emission from Parametrically Excited Cavities, Phys. Rev. Lett. 130, 064002 (2023)
2) K. Papatryfonos, M. Ruelle, C. Bourdiol, A. Nachbin, J.W.M. Bush, and M. Labousse. Hydrodynamic superradiance in wave-mediated cooperative tunneling, Communications Physics 5, 1, 142, (2022)
More recently, we showed that the static Bell inequality is violated by correlated droplets in certain geometries, where the geometry plays the role of the measurement setting in each side of the experiment. This is the first time that such inequalities are violated in a classical system that involves spatially-separated discrete particles, and a publication in currently under review to report these new results.
As a basic research project, we firstly aim to provide novel physical ideas that may advance our understanding of the laws of nature. Our long-term goal is that these ideas that we provide can also be tested by future large-scale quantum mechanical experiments that might modify our most fundamental theories in physics. By providing detailed analogs and explanations of how the correlations are developed in the fluidic systems, we aim to motivate such future investigations.Moreover by providing laboratory-scale analogs of complicated quantum phenomena that can be filmed using conventional cameras, we provide physical intuition of these phenomena, and thus a powerful educational and inspirational tool for young scientists and students.