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Quantum-Atom Optics Downunder (QAO)

Atomic Correlations From the Dissociation of a Molecular Bose-Einstein Condensate

S. L. W. Midgley, Sebastian Wüster, Matthew J. Davis, M. K. Olsen, Karen V. Kheruntsyan

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The dissociation of a molecular Bose-Einstein condensate into its constituent particles is a process analogous to parametric down-conversion in optics. However, there is additional interest in the fact that the particles are massive, and may obey either bosonic or fermionic statistics. We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to analyse the correlations present in recent experiments. We also perform calculations using stochastic phase-space methods for the bosonic case and compare the results of the two methods.

DOI
10.1364/qao.2007.qwe23

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arXiv:0910.4440•Europhysics Letters (EPL)•Nov 1, 2010•10 citations
The dissociation of a molecular Bose-Einstein condensate into its constituent particles is a process analogous to parametric down-conversion in optics. However, there is additional interest in the fact that the particles are massive, and may obey either bosonic or fermionic statistics. We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to analyse the correlations present in recent experiments. We also perform calculations using stochastic phase-space methods for the bosonic case and compare the results of the two methods.
We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one-, two-, and three-dimensional geometries and analyze the role of dimensionality on the atom production rate as a function of the dissociation energy. As well as determining the populations and coherences of the atoms, we calculate the correlations that exist between atoms of opposite momenta, including the column density correlations in three-dimensional systems. We compare the results with those of the undepleted molecular field approximation and argue that the latter is most reliable in fermionic systems and in lower dimensions. In the bosonic case we compare the pairing mean-field results with exact calculations using the positive-PPP stochastic method and estimate the range of validity of the pairing mean-field theory. Comparisons with similar first-principle simulations in the fermionic case are currently not available, however, we argue that the range of validity of the present approach should be broader for fermions than for bosons in the regime where Pauli blocking prevents complete depletion of the molecular condensate.
We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics---the positive-PPP representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strengths of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions, which can be problematic for the positive-PPP method. We find that the truncated Wigner method mostly agrees with the positive-PPP simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.
We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-PPP representation method. This allows us to provide an exact treatment of the molecular field depletion and sss-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process---which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion---is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.
Abstract The measurement and characterisation of correlation functions has recently become one of the central themes in the studies of ultracold quantum gases. By probing complex many-body states of these interacting systems, correlation functions facilitate the most in-depth understanding of the underlying physics, not accessible through simple density profile measurements. In this thesis, we study the dynamics of second-order correlation functions for atoms created in pair-production processes such as molecular dissociation and atomic four-wave mixing. More specifically, in Chapter 3 we analyse the dynamics of correlated atom pairs created via controlled dissociation of a Bose-Einstein condensate of diatomic molecules. The atomic constituents can be either a pair of bosonic or fermionic atoms. The process provides a matter-wave analog of parametric down-conversion with photons, which was pivotal in the advancement of quantum optics by enabling experimental demonstrations of the famous Einstein-Podolsky-Rosen paradox and violations of a classical Bell inequality. The atom-optics analogues of parametric down-conversion make it possible to envisage similar demonstrations using ensembles of massive particles in quantum gas regimes. In the case of fermionic constituents, molecular dissociation offers the possibility of a new paradigm in fermionic quantum-atom optics. By aiming at experimentally realistic modelling, we examine the role of spatial inhomogeneity of harmonically trapped molecular condensates on the strength and the shape of atom-atom correlations. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the short-time asymptotic behaviour of the second-order correlation functions and for relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparisons with the numerical results, which incorporate the molecular depletion and s-wave scattering interactions, show that the analytic approaches employed here capture the main underlying physics and provide useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate. In Chapter 4, we study highly anisotropic molecular condensates in order to quantify the effects of bosonic stimulation and fermionic Pauli blocking on the dissociation dynamics. We show that the difference in quantum statistics of the atomic constituent is manifest as complementary geometric structures in the density profiles of the dissociated atoms. Atomic bosons are preferentially emitted along the long axis of the molecular condensate due to bosonic stimulation, while atomic fermions are preferentially emitted along the short axis due to Pauli blocking. This anisotropy potentially simplifies the measurement of correlations between the atoms through relative number squeezing. In Chapter 5 we apply our analytic approaches to a related problem of atomic four-wave mixing and analyze atom-atom correlations in the s-wave scattering halo of two colliding condensates. The results in the short-time limit are in agreement with the first-principles simulations using the positive-P representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 2007]. The final chapter of the thesis, Chapter 6, is devoted to the first application of the Gaussian fermionic phase-space method to a dynamical simulation of a multimode fermion-boson system. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems. We have applied the Gaussian phase-space method to the problem of molecular dissociation in the simplest uniform case and demonstrated a successful treatment of large molecular condensates containing up to 10^4 molecules and 10^3 distinct atomic modes. Simulating a system in such a large Hilbert space would be impossible using a more traditional exact numerical method based on the number-state representation. Our simulations reveal, in the long-time limit, significant deviations of atom-molecule and molecule-molecule correlations from the predictions of approximate pairing mean-field theories, as well as significant departures of atom-atom correlations from Wick's factorisation scheme. We have examined the accuracy and limitations of the fermionic phase-space results by comparison with the number-state calculations for small-size systems and via the analysis of conserved quantities. Future extensions of this work will have to incorporate spatial inhomogeneity and s-wave scattering interactions in order to enable first-principles dynamical simulations of a broader class of fermionic systems of current experimental interest. To this end, we have implemented a phase-space treatment of the Fermi-Hubbard model and present some exploratory simulations of Hubbard dynamics.
An unstable condensate of diatomic molecules will coherently disassociate into correlated pairs of atoms. This dissociation process exhibits very rich quantum dynamics depending on the quantum statistics of the constituent atoms. We show that in the case of bosonic atoms Bose enhancement can lead to stimulated dissociation, whereas, in the case of fermions Pauli blocking of the available states and a buildup of coherence between molecules and atom pairs can give rise to incomplete dissociation of the molecules and transient association-dissociation oscillations.
We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.