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arXiv:0809.3842 · Physical Review A

Directional effects due to quantum statistics in dissociation of elongated molecular condensates

Magnus Ögren, Craig M. Savage, Karen V. Kheruntsyan

Published Apr 23, 2009• 9 citations
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Abstract

Ultracold clouds of dimeric molecules can dissociate into quantum mechanically correlated constituent atoms that are either both bosons or both fermions. We theoretically model the dissociation of two-dimensional anisotropic molecular condensates for which this difference manifests as complementary geometric structures of the dissociated atoms. Atomic bosons are preferentially emitted along the long axis of the molecular condensate, while atomic fermions are preferentially emitted along the short axis. This anisotropy potentially simplifies the measurement of correlations between the atoms through relative number squeezing.

DOI
10.1103/physreva.79.043624

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Ultracold clouds of dimeric molecules can dissociate into quantum mechanically correlated constituent atoms that are either both bosons or both fermions. We theoretically model the dissociation of two-dimensional anisotropic molecular condensates for which this difference manifests as complementary geometric structures of the dissociated atoms. Atomic bosons are preferentially emitted along the long axis of the molecular condensate, while atomic fermions are preferentially emitted along the short axis. This anisotropy potentially simplifies the measurement of correlations between the atoms through relative number squeezing.
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.
We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.
We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair correlations in the short-time limit. Both fermionic and bosonic statistics of the constituent atoms are considered. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the asymptotic behavior of the second-order correlation functions and for the relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparison with the numerical results shows that the analytic approach employed here captures the main underlying physics and provides useful insights into the dynamics of dissociation for conversion efficiencies up to 1010%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.
We study a fermionic atom optics counterpart of parametric down-conversion with photons. This can be realized through dissociation of a Bose-Einstein condensate of molecular dimers consisting of fermionic atoms. We present a theoretical model describing the quantum dynamics of dissociation and find analytic solutions for mode occupancies and atomic pair correlations, valid in the short time limit. The solutions are used to identify upper bounds for the correlation functions, which are applicable to any fermionic system and correspond to ideal particle number-difference squeezing.
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.
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.