This thesis proposes two complementary scenarios to observe Bell correlations in the motion of two macroscopically separated material particles. Both are based on the gradual dissociation of ultracold Feshbach molecules and result in macroscopic delocalizations of the single-atom states. By giving a full account of these scenarios, including the coupled-channel description of the Feshbach dissociation, the optically guided dispersive propagation, interferometric processing and the final position measurements, I demonstrate for both cases their potential to violate a Bell inequality under experimentally viable conditions that correspond to delocalizations and interatomic separations on the order of centimeters.
This thesis proposes two complementary scenarios to observe Bell correlations in the motion of two macroscopically separated material particles. Both are based on the gradual dissociation of ultracold Feshbach molecules and result in macroscopic delocalizations of the single-atom states. By giving a full account of these scenarios, including the coupled-channel description of the Feshbach dissociation, the optically guided dispersive propagation, interferometric processing and the final position measurements, I demonstrate for both cases their potential to violate a Bell inequality under experimentally viable conditions that correspond to delocalizations and interatomic separations on the order of centimeters.
We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.
The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.
The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.
We describe the dissociation of a diatomic Feshbach molecule due to a time-varying external magnetic field in a realistic trap and guide setting. An analytic expression for the asymptotic state of the two ultracold atoms is derived, which can serve as a basis for the analysis of dissociation protocols to generate motionally entangled states. For instance, the gradual dissociation by sequences of magnetic field pulses may delocalize the atoms into macroscopically distinct wave packets, whose motional entanglement can be addressed interferometrically. The established relation between the applied magnetic field pulse and the generated dissociation state reveals that square-shaped magnetic field pulses minimize the momentum spread of the atoms. This is required to control the detrimental influence of dispersion in a recently proposed experiment to perform a Bell test in the motion of the two atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].
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.
The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.