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arXiv:0901.4529 · Physical Review A

Preparation of atomic Fock states by trap reduction

M. Ll. Pons, Adolfo del Campo, Juan Gonzalo Muga, Mark G. Raizen

Published Mar 31, 2009• 26 citations
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Abstract

We describe the preparation of atom-number states with strongly interacting bosons in one dimension or spin-polarized fermions. The procedure is based on a combination of weakening and squeezing of the trapping potential. For the resulting state, the full atom-number distribution is obtained. Starting with an unknown number of particles ${N}_{i}$, we optimize the sudden change in the trapping potential which leads to the Fock state of ${N}_{f}$ particles in the final trap. Nonzero temperature effects as well as different smooth trapping potentials are analyzed. A simple criterion is provided to ensure the robust preparation of the Fock state for physically realistic traps.

DOI
10.1103/physreva.79.033629

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We describe the preparation of atom-number states with strongly interacting bosons in one dimension or spin-polarized fermions. The procedure is based on a combination of weakening and squeezing of the trapping potential. For the resulting state, the full atom-number distribution is obtained. Starting with an unknown number of particles Ni{N}_{i}Ni​, we optimize the sudden change in the trapping potential which leads to the Fock state of Nf{N}_{f}Nf​ particles in the final trap. Nonzero temperature effects as well as different smooth trapping potentials are analyzed. A simple criterion is provided to ensure the robust preparation of the Fock state for physically realistic traps.
We study the production of low-atom-number Fock states by sudden reduction of the potential trap in a one-dimensional strongly interacting (Tonks-Girardeau) gas. The fidelity of the Fock-state preparation is characterized by the average and variance of the number of trapped atoms. Two different methods are considered: making the trap shallower (atom culling [Dudarev et al., Phys. Rev. Lett. 98, 063001 (2007)], also termed ``trap weakening'' here) and making the trap narrower (trap squeezing). When used independently, the efficiency of both procedures is limited as a result of the truncation of the final state in momentum or position space with respect to the ideal atom-number state. However, their combination provides a robust and efficient strategy to create ideal Fock states.
We investigate the possibility of forming high-fidelity atomic Fock states by gradual reduction of a quasi-one-dimensional trap containing spin-polarized fermions or strongly interacting bosons in the Tonk-Girardeau regime. Making the trap shallower and simultaneously squeezing it can lead to the preparation of an ideal atomic Fock state as one approaches either the sudden or the adiabatic limits. Nonetheless, the fidelity of the resulting state is shown to exhibit nonmonotonic behavior with the time scale in which the trapping potential is changed.
We describe methods for the fast production of highly coherent-spin-squeezed many-body states in bosonic Josephson junctions. We start from the known mapping of the two-site Bose-Hubbard (BH) Hamiltonian to that of a single effective particle evolving according to a Schr\"odinger-like equation in Fock space. Since, for repulsive interactions, the effective potential in Fock space is nearly parabolic, we extend recently derived protocols for shortcuts to adiabatic evolution in harmonic potentials to the many-body BH Hamiltonian. A comparison with current experiments shows that our methods allow for an important reduction in the preparation times of highly squeezed spin states.
To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals.The simplest way to compose the basis is to choose a finite set of single-particle wave functions and find all possible distributions of a given number of particles in these states.It is known, however, that this construction leads to very inaccurate results since it does not take into account different many-body states having the same energy on equal footing.Here we present a fast and surprisingly simple algorithm for generating the many-body Fock basis built from many-body Fock states having the lowest non-interacting energies.The algorithm is insensitive to details of the distribution of single-particle energies and it can be used for an arbitrary number of particles obeying bosonic or fermionic statistics.Moreover, it can be easily generalized to a larger number of components.Taking as a simple example the system of two ultra-cold bosons in an anharmonic trap, we show that exact calculations in the basis generated with the algorithm are substantially more accurate than calculations performed within the standard approach.
We theoretically analyze atom interferometry based on trapped ultracold atoms and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows us to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom-number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms and the multiconfigurational time-dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.
We develop a dissipative quantum state preparation scheme for the creation of phase- and number-squeezed states. It utilizes ultracold atoms in a double-well configuration immersed in a background Bose-Einstein condensate, with the latter consisting of an atom species different from the atoms in the double well and acting as a dissipative quantum reservoir. We derive a master equation for this system starting from microscopic physics and show that squeezing develops on a time scale proportional to 1/N1/N1/N, where NNN is the number of particles in the double well. This scaling, caused by bosonic enhancement, allows us to make the time scale for the creation of squeezed states very short. The lifetime of squeezed states is limited by dephasing arising from the intrinsic structure of the setup. However, the dephasing can be avoided by stroboscopically switching the driving off and on. We show that this approach leads to robust stationary squeezed states. Finally, we provide the necessary ingredients for a potential experimental implementation by specifying a parameter regime for rubidium atoms that leads to squeezed states.