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Bulletin of the American Physical Society

Numerical Calculations of Small to Large Numbers of Cold Fermions and Bosons in a 1D Double Well Potential

Thomas H. Bergeman

Published Jun 11, 2015• 0 citations
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Abstract In a previous paper, Das et al (2013 J. Phys. B: At. Mol. Opt. Phys . 46 035501), it was shown that the unitary quantum phase operators play a particularly important role in quantum dynamics of bosons and fermions in a one-dimensional (1D) double-well (DW) when the number of particles is small. In this paper, we define the standard quantum limit (SQL) for phase and number fluctuations, and describe two-mode squeezing for number and phase variables. The usual two-mode number squeezing parameter, also used to describe two-mode entanglement of a quantum field, is defined considering phase as a classical variable. However, when phase is treated as a unitary quantum-mechanical operator, number and phase operators satisfy an uncertainty relation. As a result, the usual definition of number squeezing parameter becomes modified. Two-mode number squeezing occurs when the number fluctuation goes below the SQL at the cost of enhanced phase fluctuation. As an application of number-phase uncertainty, we consider bosons or fermions trapped in a quasi-1D DW potential interacting via a 3D finite-range two-body interaction potential with large scattering length a s . Under tight-binding or two-mode approximation, we describe in detail the effects of the range of interaction on the quantum dynamics and number-phase uncertainty in the strongly interacting or unitarity regime a s → ± ∞ . Our results show intriguing coherent dynamics of number-phase uncertainty with number squeezing for bosons and ph squeezing for fermions. Our results may be important for exploring new quantum interferometry, Josephson oscillations, Bose–Hubbard and Fermi–Hubbard physics with ultracold atoms in DW potentials or DW optical lattices. Particularly interesting will be the question of the importance of quantum phase operators in two-atom interferometry and entanglement.

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Abstract We use the two mode approximation for a interacting one-dimensional spinless soft core bosons and one half spin fermions in a double-well potential with a large central barrier. We include all the on-site boson-boson, fermion-fermion and boson-fermion repulsive contact potential represented by delta-function and considered bosonic and fermionic isotopes of ytterbium(Yb) 170 Yb and 171 Yb respectively. By means of this approximation, we find that in the regime λ BF > λ BB give rise to a immiscible phase and in the regime λ BB ≥ λ BF give rise to a miscible phase, that is characterized by a temporal overlap of the bosonic and fermionic probability densities. We also report that due to the Bose-Fermi interaction, the system presents an apparent destruction of the collapse-revival oscillation of boson density probability at least in the ranges investigated.

Journal of Physics Communications•Jan 27, 2022•4 citations
Abstract In a previous paper, Das et al (2013 J. Phys. B: At. Mol. Opt. Phys . 46 035501), it was shown that the unitary quantum phase operators play a particularly important role in quantum dynamics of bosons and fermions in a one-dimensional (1D) double-well (DW) when the number of particles is small. In this paper, we define the standard quantum limit (SQL) for phase and number fluctuations, and describe two-mode squeezing for number and phase variables. The usual two-mode number squeezing parameter, also used to describe two-mode entanglement of a quantum field, is defined considering phase as a classical variable. However, when phase is treated as a unitary quantum-mechanical operator, number and phase operators satisfy an uncertainty relation. As a result, the usual definition of number squeezing parameter becomes modified. Two-mode number squeezing occurs when the number fluctuation goes below the SQL at the cost of enhanced phase fluctuation. As an application of number-phase uncertainty, we consider bosons or fermions trapped in a quasi-1D DW potential interacting via a 3D finite-range two-body interaction potential with large scattering length a s . Under tight-binding or two-mode approximation, we describe in detail the effects of the range of interaction on the quantum dynamics and number-phase uncertainty in the strongly interacting or unitarity regime a s → ± ∞ . Our results show intriguing coherent dynamics of number-phase uncertainty with number squeezing for bosons and ph squeezing for fermions. Our results may be important for exploring new quantum interferometry, Josephson oscillations, Bose–Hubbard and Fermi–Hubbard physics with ultracold atoms in DW potentials or DW optical lattices. Particularly interesting will be the question of the importance of quantum phase operators in two-atom interferometry and entanglement.
We use the two mode approximation for a interacting one-dimensional spinless soft core bosons and one half spin fermions in a double-well potential with a large central barrier. We include all the on-site boson-boson, fermion-fermion and boson-fermion repulsive contact potential represented by delta-function and considered bosonic and fermionic isotopes of ytterbium(Yb) 170Yb^{170}Yb170Yb and 171Yb^{171}Yb171Yb respectively. By means of the approximation, we find that in the regime UBF>UBBU_{BF}>U_{BB}UBF​>UBB​ give rise to a immiscible phase and in the regime UBB≥UBFU_{BB}\geq U_{BF}UBB​≥UBF​ give rise to a miscible phase, that is characterized by a temporal overlap of the bosonic and fermionic probability densities. We also report that due to the Bose-Fermi interaction, the system presents an apparent destruction of the collapse-revival oscillation of boson density probability at least in the ranges investigated.
Abstract We use the two mode approximation for a interacting one-dimensional spinless soft core bosons and one half spin fermions in a double-well potential with a large central barrier. We include all the on-site boson-boson, fermion-fermion and boson-fermion repulsive contact potential represented by delta-function and considered bosonic and fermionic isotopes of ytterbium(Yb) 170 Yb and 171 Yb respectively. By means of this approximation, we find that in the regime λ BF > λ BB give rise to a immiscible phase and in the regime λ BB ≥ λ BF give rise to a miscible phase, that is characterized by a temporal overlap of the bosonic and fermionic probability densities. We also report that due to the Bose-Fermi interaction, the system presents an apparent destruction of the collapse-revival oscillation of boson density probability at least in the ranges investigated.