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arXiv:1009.0640 · Physical Review A

Atomic Fock states by gradual trap reduction: From sudden to adiabatic limits

D. Sokolovski, M. Ll. Pons, Adolfo del Campo, Juan Gonzalo Muga

Published Jan 18, 2011• 11 citations
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Abstract

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.

DOI
10.1103/physreva.83.013402

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•Jan 1, 2016•0 citations
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 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 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.
Adiabatic techniques can be used to control quantum states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may be isolated from the environment only for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity can be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks–Girardeau gases.
A harmonically trapped, ultracold, one-dimensional (1D) spin-1 Bose gas with strongly repulsive or attractive 1D even-wave interactions induced by a three-dimensional (3D) Feshbach resonance is studied. The exact ground state, a hybrid of Tonks-Girardeau (TG) and ideal Fermi gases, is constructed in the TG limit of infinite even-wave repulsion by a spinor Fermi-Bose mapping to a spinless ideal Fermi gas. It is then shown that in the limit of infinite even-wave attraction this same state remains an exact many-body eigenstate, now highly excited relative to the collapsed generalized McGuire-cluster ground state, showing that the hybrid TG state is completely stable against collapse to this cluster ground state under a sudden switch from infinite repulsion to infinite attraction. It is shown to be the TG limit of a hybrid super-Tonks-Girardeau (STG) state, which is metastable under a sudden switch from finite but very strong repulsion to finite but very strong attraction. It should be possible to create it experimentally by a sudden switch from strongly repulsive to strongly attractive interaction, as in the recent Innsbruck experiment on a spin-polarized bosonic STG gas. In the case of strong attraction, there should also exist another STG state of much lower energy, consisting of strongly bound dimers, a bosonic analog of a recently predicted STG state which is an ultracold gas of strongly bound bosonic dimers of fermionic atoms, but it is shown that this STG state cannot be created by such a switch from strong repulsion to strong attraction.
Fermi gases confined in tight one-dimensional waveguides form two-particle bound states of atoms in the presence of a strongly attractive interaction. Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi gas, we demonstrate that a stable excited state with no pairing between attractive fermionic atoms can be realized by a sudden switch of interaction from the strongly repulsive regime to strongly attractive regime. Such a state is an exact fermionic analog of the experimentally observed super-Tonks-Girardeau state of bosonic Cesium atoms [Science 325, 1224 (2009)] and should be possible to be observed by the experiment. The frequency of the lowest breathing mode of the fermionic super-Tonks-Girardeau gas is calculated as a function of the interaction strength, which could be used as a detectable signature for the experimental observation.
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.