Due to their coherence properties, dilute atomic gas Bose-Einstein condensates seem a versatile platform for controlled creation of mesoscopically entangled states with a large number of particles and allow controlled studies of their decoherence. However, the creation of such states intrinsically involves many-body quantum dynamics that cannot be captured by mean-field theory and, thus, invalidates the most common methods for the description of condensates. We follow up on a proposal in which a condensate cloud as a whole is brought into a superposition of two different spatial locations by mapping entanglement from a strongly interacting Rydberg atomic system onto the condensate using off-resonant laser dressing [Phys. Rev. Lett. 115 040401 (2015)]. A variational many-body ansatz akin to recently developed multiconfigurational methods allows us to model this entanglement mapping step explicitly, while still preserving the simplicity of mean-field physics for the description of each branch of the superposition. In the second part of the article, we model the decoherence process due to atom losses in detail. Altogether we confirm earlier estimates that tightly localized clouds of 400 atoms can be brought into a quantum superposition of two locations about $3\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ apart and remain coherent for about 1 ms.
Due to their coherence properties, dilute atomic gas Bose-Einstein condensates seem a versatile platform for controlled creation of mesoscopically entangled states with a large number of particles and allow controlled studies of their decoherence. However, the creation of such states intrinsically involves many-body quantum dynamics that cannot be captured by mean-field theory and, thus, invalidates the most common methods for the description of condensates. We follow up on a proposal in which a condensate cloud as a whole is brought into a superposition of two different spatial locations by mapping entanglement from a strongly interacting Rydberg atomic system onto the condensate using off-resonant laser dressing [Phys. Rev. Lett. 115 040401 (2015)]. A variational many-body ansatz akin to recently developed multiconfigurational methods allows us to model this entanglement mapping step explicitly, while still preserving the simplicity of mean-field physics for the description of each branch of the superposition. In the second part of the article, we model the decoherence process due to atom losses in detail. Altogether we confirm earlier estimates that tightly localized clouds of 400 atoms can be brought into a quantum superposition of two locations about 3\ensuremathμm apart and remain coherent for about 1 ms.
We studied the creation of coherent atomic ensembles by various means, allof which are either already demonstrated experimentally or within reach ofcurrent experiments. We investigated the dynamics of the outcoupling of acoherent beam from an atomic Bose-Einstein condensate. Since this problemis well treated in present literature, we focused on another aspect of proposedatom-laser schemes, the pumping. To this end, we investigated the merging ofindependent condensates and paid particular attention to the role of the relativephase. We found that it emerges as a key parameter during the merging process,almost solely defining the resulting dynamics. More concretely, the phasedifference determines the depth of an adiabatically formed soliton as well as thedynamics of a dipole oscillation of the atomic cloud, which builds up during themerging process. Under the assumption of a coherent cooling, such as evaporationof higher energy atoms from the ensemble, we were able to empiricallyfind an analytic formula for the phase of the final condensate. We studied themerging as an independent process, not necessarily linked to the atom laseritself. Our results might shed light onto new, non-destructive ways of readingout phase-differences between condensates as it is necessary in matter-wavespectroscopy. Although not related to our work, it is worth mentioning thatin the mean-time, a different pumping mechanism was demonstrated. It relieson two electronic transitions, with a reservoir condensate and a separate lasingcondensate [74]. We turned towards a different way of producing matter wavepulses altogether, namely superradiance from condensates, which shows otherpromising aspects, such as well defined populations and momenta of the createdpulses. We constructed a quantum treatment for the early stages of the process,which, as we have shown, is not well described within the available mean-fieldmodels. This semi-classical model can, however, produce quantum expectationvalues by means of averaging over randomly seeded trajectories. We used thisrelations to investigate the statistics of delay– and passage-times of superradiantpulses. Beyond the mean-field treatment of the problem, the quantum modelpredicts long range order as well as atomic bunching in the side-modes and enhancedcross-correlations between forward and backwards scattered atoms. Inthe strong pulse regime, the two counter-propagating clouds become entangledand the number difference between them is squeezed.4.6.2 OutlookThe experimental verification of our results is within reach of current experiments,and the tools available to probe Bose-Einstein condensates are advancingat a fast rate. As far as our studies are concerned, there are still open questions.We found that, in general, the merging of condensates is related to the formationof a soliton. The decay of such a structure is a topic of current debate, but theconsensus that this depends highly on the geometry of the trapping potentialsused seems reached.We investigated the early stage of superradiance from condensates and it isnatural to ask what is to expect for later stages, or in other situations wheredepletion of the primary condensate, population of higher order side-modes or120interaction between end-fire modes become relevant. Our results suggest thatthe exotic correlations we found decay with time, but this is not conclusive
The central theme of this thesis is that of coherence in bosonic matter-wave fields. Analogous to optical coherence; the measure of the capacity of a photonic beam to produce fringes upon interference; matter-wave coherence is in many ways the defining characteristic of the BEC phase of identical massive bosons. Its study therefore plays a critical role in the quest to better understand the physics of ultra-cold quantum gases, which has been the goal of this research. This work approaches coherence from a number of different angles and is for this reason presented in two parts. The first of these delves into the physics of perfectly coherent matterwave fields which are adequately described by ‘mean field’ equations, while the second is devoted to origins and repercussions of the diminished coherence evident in actual atom laser experiments. The presentation of the original work of this project begins with a detailed study of the interaction between an atomic and a molecular condensate, coherently coupled at zero temperature via one of several possible mechanisms (a Feshbach resonance, for example) in three spatial dimensions. Despite the presence of repulsive scattering interaction between the atoms, the mean-field equations of motion are known to support bright solitary waves — time-independent solutions which remain localised even in the absence of a trapping potential. (These solutions are the matter-wave analogue of spatio-temporal solitons in quadratic nonlinear media, but can also represent stationary states of the Schr¨odinger-Newton equations describing bosons interacting via a gravitational field.) Ignoring all interactions save the repulsive inter-atomic scattering mentioned, a variational ansatz approach is employed to analytically approximate these stationary solutions using Gaussian density distributions of the atomic and molecular clouds. By evolving these approximate solutions numerically, a comprehensive map of the accessible parameter space is constructed, showing primarily stable localised propagation. Parameter space regions where the approximate Gaussian solutions display strong ‘breathing’ oscillations are identified, and a modified ansatz having exponentially decaying tails is found to dramatically reduce the amplitude of these oscillations. Finally, by seeding a numerical relaxation algorithm with our Gaussian solutions, we find that the only parameter space region in which the approximate solutions diffuse under propagation is also devoid of exact localised stationary solutions. The discussion then proceeds beyond the scope of mean field theory, and turns to a detailed treatment of the quantum mechanical observable corresponding to the centre of mass of systems of identical particles. Firstly, careful consideration is given to its operational definition in the presence of fluctuating particle numbers. Possible pitfalls due to naive approximations when the number fluctuations are large are also addressed. Attention is then given to the fundamental quantum noise associated with this variable, which provides a physical mechanism for diminished first order coherence in degenerate Bose gases, even at zero temperature. Characteristic lower bounds (standard quantum limits) to the resulting mean position uncertainty are identified both for systems of identical bosons and identical fermions with comparable density profiles. Interestingly, fermions are found to have an intrinsically lower mean-position uncertainty than bosons, a fact which is attributed to the action of Pauli repulsion between atoms confined to a fixed density distribution. The results of numerical simulations of the exact quantum evolution of mean position variance are then presented. These demonstrate firstly the quantum diffusion of the mean position of one dimensional matter-wave solitons and secondly the evolution of variance in the centre of mass of a Bose gas undergoing forced evaporative cooling. Finally, attention is paid to the fact that the Penrose-Onsager criterion, which essentially equates Bose condensation with perfect first-order matter-wave coherence, fails to correctly detect the presence of BEC when a priori knowledge of the exact condensate mode is imperfect or unavailable. Insight is gained by drawing analogies between this criterion and entropic measures of entanglement between particular system subspaces. This motivates employment of the concept of entanglement of formation as a means to providing a more accurate measure of condensation in the general case of mixed system states. Unfortunately, this new measure remains adversely sensitive to superpositions of condensate modes. For this reason, alternative criteria based on higher order particle number correlation functions are also proposed.
In Rydberg dressed ultracold gases, ground-state atoms inherit properties of a weakly admixed Rydberg state, such as sensitivity to long-range interactions. We show that through hyperfine-state-dependent interactions, a pair of atom clouds can evolve into a spin and subsequently into a spatial mesoscopic superposition state: The pair is in a coherent superposition of two configurations, with cloud locations separated by micrometers. The mesoscopic nature of the state can be proven with absorption imaging, while the coherence can be revealed though recombination and interference of the split wave packets.
Abstract We predict hyper-entanglement generation by binary scattering of mesoscopic bound states, considering solitary waves in Bose–Einstein condensates containing thousands of identical Bosons. For it to occur, the underlying many-body Hamiltonian must not be integrable, and the pre-collision quantum state of the solitons needs to be fragmented. Under these conditions, we show that the post-collision state will be hyper-entangled in spatial degrees of freedom and atom number within solitons, for realistic parameters. The effect links aspects of non-linear systems and quantum-coherence and the entangled post-collision state challenges present entanglement criteria for identical particles. Our results are based on simulations of colliding quantum solitons in a quintic interaction model beyond the mean-field, using the truncated Wigner approximation.
The observation of Bose-Einstein condensation (BEC) in dilute atomic gases was the realization of many long-standing goals: (1) to cool neutral atoms into the ground state of the system, thus exerting ultimate control over the motion and position of atoms limited only by Heisenberg's uncertainty relation; (2) to generate a coherent sample of atoms all occupying the same quantum state (this was subsequently used to realize an atom laser, a device which generates coherent matter waves); and (3) to create a quantum fluid with properties quite different from the quantum liquids He-3 and He-4. This provides a test-ground for many-body theories of the dilute Bose gas which were developed many decades ago, but never tested experimentally.
We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small-particle-number cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat-state fidelities.