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arXiv:0711.1829 · Physical Review A

Atom Fock-state preparation by trap reduction

Adolfo del Campo, Juan Gonzalo Muga

Published Aug 20, 2008• 20 citations
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Abstract

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.

DOI
10.1103/physreva.78.023412

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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 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 consider an ultracold atomic gas trapped in a one-dimensional harmonic oscilla- tor potential. We study the transition from a Bose-Einstein condensate, in the small atom-atom interaction limit, to a strongly interacting Tonks-Girardeau gas, as the interaction is varied from zero to large values. The response of the system against a monopolar perturbation is characterized by the moments of the dynamic structure function. The calculations have been done by direct diagonalization of the second quantized many-body Hamiltonian in a truncated Fock space. The corresponding virial theorem for the many-body states has been employed to cross-check the validity of our numerical techniques.
We report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.
Abstract Using the so-called operator product expansion to lowest order, we extend the work in Campbell et al (2015 Phys. Rev. Lett 114 125302) by deriving a simple analytical expression for the long-time asymptotic one-body reduced density matrix during free expansion for a one-dimensional system of bosons with large atom number interacting through a repulsive delta potential initially confined by a potential well. This density matrix allows direct access to the momentum distribution and also to the mass current density. For initially confining power-law potentials we give explicit expressions, in the limits of very weak and very strong interaction, for the current density distributions during the free expansion. In the second part of the work we consider the expansion of ultracold gas from a confining harmonic trap to another harmonic trap with a different frequency. For the case of a quantum impenetrable gas of bosons (a Tonks–Girardeau gas) with a given atom number, we present an exact analytical expression for the mass current distribution (mass transport) after release from one harmonic trap to another harmonic trap. It is shown that, for a harmonically quenched Tonks–Girardeau gas, the current distribution is a suitable collective observable and under the weak quench regime, it exhibits oscillations at the same frequencies as those recently predicted for the peak momentum distribution in the breathing mode. The analysis is extended to other possible quenched systems.