Final Report Summary - QUANTUMDYNAMICS (Characterisation of the basic elements of BEC dynamics beyond mean-field)
The project has studied the dynamical behaviour of artificially made ultracold atom clouds, such as Bose-Einstein condensates. These are the coldest objects in the universe known to us, far colder than anything occurring naturally, and have been one of the most robustly expanding fields of research in physics in the last 20 years. This is a whole new state of matter that has not been known in the past, and that has remarkable properties. The majority of atoms in the cloud, trapped and suspended in vacuum by a magnetic or optical trap, behave as a single coherent matter wave, called the condensate. While being composed of normal atoms, their wavelength is so long that they overlap with each other and lose distinguishable identity, acting in many ways as a laser field. Such objects push the boundaries of what we know of matter, at the opposite end of the energy scale to that studied by particle physicists.
Our research in this project was focused on understanding those atoms that are scattered out of the underlying condensate. These are expected to consist in large part of pairs of counter-propagating atoms, which may be a usable source of quantum correlated and entangled massive particles. While inherently quantum states that display entanglement and quantum correlations have a long experimental history this has been primarily work with photons. The study now of massive particles in such inherently quantum states is an avenue to investigate the very fundamentals of how matter behaves in the universe.
The project consisted of three kinds of studies. The first was in collaboration with a leading experiment in the field, the Palaiseau metastable helium experiment, where simulations of the quantum dynamics of the experiment were carried out using methods developed in this project. The second was independent theoretical work which aimed to understand aspects of the ultracold gases beyond a mean field description that have not yet been observed, and to predict under what conditions they can be seen in future or existing experiments. The third was to push forward the development of new methods for the numerical simulation of the quantum dynamics of these systems.
The most significant results obtained in the course of the project have been:
1. Our collaboration with the Palaiseau metastable helium experiment was able to demonstrate the presence of strongly non-classical correlations in atom pairs scattered from Bose-Einstein condensation (BEC) collisions. The first experiment showed that the counter-propagating pairs have sub-shot noise fluctuations in the relative number (Jaskula et al, Phys. Rev. Lett. 105, 190402 (2010)). The second experiment showed a strong violation of the Cauchy-Schwartz inequality, which proves that the positions of the halo atoms cannot be described by any classical wave field (Kheruntsyan et al, Phys. Rev. Lett. 108, 260401 (2012)). This project was responsible for theory and all the numerical simulations of the system, which contains 100 000 interacting atoms in each shot on average. The work was published as two papers in the leading physics journal Physical Review Letters and also attracted a feature article on our research by the eminent scientist Mihai Macovei in the commentary journal Physics (M.A. Macovei 'Matter Waves and Quantum Correlations', Physics 5, 70 (2012)). These experiments are an analogue to the watershed quantum optics experiments with nonclassical light fields from several decades ago. The long-term goal is to follow this path of ever stronger non-classicality and achieve violations of Bell inequalities with massive particles in these experiments. The plan is to use a setup similar to the Rarity-Tapster experiments of quantum optics where the entanglement is between pairs arriving at the measuring apparatus or not. This test would have a new quality in comparison with Bell and Einstein-Podolsky-Rosen (EPR) tests that use just the spins of massive particles, because one would have an actual entanglement between states of different rest mass, not just a spin quantum number. That would violate the particle number superselection rule with massive particles, which has been oftentimes raised to the status of a fundamental principle.
2. We have also carried out an in-depth theory and numerical analysis of the many factors responsible for degradation of the pair entanglement in BEC collisions (Deuar et al, arXiv:1301.3726). It was found that the essential spoiling ingredient for pair degradation was the non-monochromaticity (many-mode nature) of the source clouds, as opposed to other spoiler candidates such as Bose enhancement, mean-field, or 'skier' effects. Importantly, while in principle any setup can produce clean pairs if it is sufficiently monochromatic, we showed that clouds that are dense enough to enter a stimulated scattering regime are far less robust to the non-monochromaticity because of the prevalence of stray unpaired atoms. This has important consequences for the design of future experiments and their interpretation. It also explains why directed-beam experiments are advantageous, and indicates that if pair degradation is too severe, it can be readily reduced by a reduction of the cloud density.
3. We have found the universal time and space behaviour of phase and density correlations in dilute Bose gases after a quantum quench in one dimension (1D), 2D and 3D. The study of this process is important because such correlations should in fact be ubiquitously present and waiting to be seen in existing experiments. A quantum quench occurs when overall parameters of the system are suddenly changed by external manipulations, so that the system finds itself in a state that is no longer well matched to the new conditions. In our case we considered what happens when the strength of the interactions among atoms is suddenly increased. This is common in ultracold atom experiments, occurring naturally during preparation of the atom clouds, but it is also something can be engineered intentionally in a controlled way. Furthermore we have discovered that the density correlations can be observed under the right conditions even with detection schemes that have a resolution many times worse than the healing length in the gas. This is the case in contemporary experiments. We have found simple expressions for these correlations in most regimes, which should be of direct interest for other studies, both experimental and theoretical on this matter.
4. We have made extensive development of the 'Stochastic time-adaptive Bogoliubov' (STAB) method for simulating the quantum dynamics of huge ensembles of scattered atoms in cold atom systems, to a greater degree even than initially envisaged in the original project. The method is now at the stage where both atoms near the source clouds and those far away can be treated properly, and the research is at the cusp of allowing for the simulation of strongly finite-temperature gases, in which the condensate fraction is negligible. It allows one to access a whole new parameter regime in such problems. The method is actually quite straightforward to implement, consisting of the evolution of coupled stochastic differential equations, and has already begun to be used by some researchers not affiliated with this project.
5. Furthermore, we have developed a method to simulate the dynamics of spin systems that is robust against an increase of the system dimension, and can treat 1D, 2D, 3D, and non-uniform spin systems on an equal footing, up to a certain useful simulation time. This is typically a time at which such a system has already significantly decohered, though not yet fully. Further development of this method may allow the simulation of the quantum dynamics of spin systems that have been previously inaccessible to exact calculations.
Contact details: Piotr Deuar, deuar@ifpan.edu.pl
Our research in this project was focused on understanding those atoms that are scattered out of the underlying condensate. These are expected to consist in large part of pairs of counter-propagating atoms, which may be a usable source of quantum correlated and entangled massive particles. While inherently quantum states that display entanglement and quantum correlations have a long experimental history this has been primarily work with photons. The study now of massive particles in such inherently quantum states is an avenue to investigate the very fundamentals of how matter behaves in the universe.
The project consisted of three kinds of studies. The first was in collaboration with a leading experiment in the field, the Palaiseau metastable helium experiment, where simulations of the quantum dynamics of the experiment were carried out using methods developed in this project. The second was independent theoretical work which aimed to understand aspects of the ultracold gases beyond a mean field description that have not yet been observed, and to predict under what conditions they can be seen in future or existing experiments. The third was to push forward the development of new methods for the numerical simulation of the quantum dynamics of these systems.
The most significant results obtained in the course of the project have been:
1. Our collaboration with the Palaiseau metastable helium experiment was able to demonstrate the presence of strongly non-classical correlations in atom pairs scattered from Bose-Einstein condensation (BEC) collisions. The first experiment showed that the counter-propagating pairs have sub-shot noise fluctuations in the relative number (Jaskula et al, Phys. Rev. Lett. 105, 190402 (2010)). The second experiment showed a strong violation of the Cauchy-Schwartz inequality, which proves that the positions of the halo atoms cannot be described by any classical wave field (Kheruntsyan et al, Phys. Rev. Lett. 108, 260401 (2012)). This project was responsible for theory and all the numerical simulations of the system, which contains 100 000 interacting atoms in each shot on average. The work was published as two papers in the leading physics journal Physical Review Letters and also attracted a feature article on our research by the eminent scientist Mihai Macovei in the commentary journal Physics (M.A. Macovei 'Matter Waves and Quantum Correlations', Physics 5, 70 (2012)). These experiments are an analogue to the watershed quantum optics experiments with nonclassical light fields from several decades ago. The long-term goal is to follow this path of ever stronger non-classicality and achieve violations of Bell inequalities with massive particles in these experiments. The plan is to use a setup similar to the Rarity-Tapster experiments of quantum optics where the entanglement is between pairs arriving at the measuring apparatus or not. This test would have a new quality in comparison with Bell and Einstein-Podolsky-Rosen (EPR) tests that use just the spins of massive particles, because one would have an actual entanglement between states of different rest mass, not just a spin quantum number. That would violate the particle number superselection rule with massive particles, which has been oftentimes raised to the status of a fundamental principle.
2. We have also carried out an in-depth theory and numerical analysis of the many factors responsible for degradation of the pair entanglement in BEC collisions (Deuar et al, arXiv:1301.3726). It was found that the essential spoiling ingredient for pair degradation was the non-monochromaticity (many-mode nature) of the source clouds, as opposed to other spoiler candidates such as Bose enhancement, mean-field, or 'skier' effects. Importantly, while in principle any setup can produce clean pairs if it is sufficiently monochromatic, we showed that clouds that are dense enough to enter a stimulated scattering regime are far less robust to the non-monochromaticity because of the prevalence of stray unpaired atoms. This has important consequences for the design of future experiments and their interpretation. It also explains why directed-beam experiments are advantageous, and indicates that if pair degradation is too severe, it can be readily reduced by a reduction of the cloud density.
3. We have found the universal time and space behaviour of phase and density correlations in dilute Bose gases after a quantum quench in one dimension (1D), 2D and 3D. The study of this process is important because such correlations should in fact be ubiquitously present and waiting to be seen in existing experiments. A quantum quench occurs when overall parameters of the system are suddenly changed by external manipulations, so that the system finds itself in a state that is no longer well matched to the new conditions. In our case we considered what happens when the strength of the interactions among atoms is suddenly increased. This is common in ultracold atom experiments, occurring naturally during preparation of the atom clouds, but it is also something can be engineered intentionally in a controlled way. Furthermore we have discovered that the density correlations can be observed under the right conditions even with detection schemes that have a resolution many times worse than the healing length in the gas. This is the case in contemporary experiments. We have found simple expressions for these correlations in most regimes, which should be of direct interest for other studies, both experimental and theoretical on this matter.
4. We have made extensive development of the 'Stochastic time-adaptive Bogoliubov' (STAB) method for simulating the quantum dynamics of huge ensembles of scattered atoms in cold atom systems, to a greater degree even than initially envisaged in the original project. The method is now at the stage where both atoms near the source clouds and those far away can be treated properly, and the research is at the cusp of allowing for the simulation of strongly finite-temperature gases, in which the condensate fraction is negligible. It allows one to access a whole new parameter regime in such problems. The method is actually quite straightforward to implement, consisting of the evolution of coupled stochastic differential equations, and has already begun to be used by some researchers not affiliated with this project.
5. Furthermore, we have developed a method to simulate the dynamics of spin systems that is robust against an increase of the system dimension, and can treat 1D, 2D, 3D, and non-uniform spin systems on an equal footing, up to a certain useful simulation time. This is typically a time at which such a system has already significantly decohered, though not yet fully. Further development of this method may allow the simulation of the quantum dynamics of spin systems that have been previously inaccessible to exact calculations.
Contact details: Piotr Deuar, deuar@ifpan.edu.pl
