Unitary quantum phase operators for bosons and fermions: a model study on the quantum phases of interacting particles in a symmetric double-well potential

Das, Biswajit; Ghosal, B.; Gupta, Subhasish Dutta; Deb, Bimalendu

doi:10.1088/0953-4075/46/3/035501

Cited by 4 publications

(17 citation statements)

References 45 publications

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“…Here we consider Barnett-Pegg [2] type quantum phase operators for matterwave of few bosons or fermions. Matter-wave phase operators were first introduced in 2013 [4]. It is shown that [4,5], for a low number of bosons or fermions, unitary nature of the phase-difference operators is important.…”

Section: Phase-operators: a Brief Reviewmentioning

confidence: 99%

“…Matter-wave phase operators were first introduced in 2013 [4]. It is shown that [4,5], for a low number of bosons or fermions, unitary nature of the phase-difference operators is important. For large number of photons or quanta, the non-unitary Carruthers-Nieto [13] phase-difference operators yield almost similar results as those due to Barnett-Pegg type unitary operator.…”

Section: Phase-operators: a Brief Reviewmentioning

confidence: 99%

“…Both of them are canonically conjugate to the number-difference operator. These two phase operators plus the numberdifference operator forms a closed algebra [4].…”

Section: Phase-operators: a Brief Reviewmentioning

confidence: 99%

“…It is then necessary to formulate the quantum phase of matter-waves with a fixed number of particles. So, it is important to study quantum atom optics under the influence of unitary phase operators in matter-waves [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Matter-wave phase operators for quantum atom optics: On the possibility of experimental verification

Adhikary,

Mal,

Saha

et al. 2021

Preprint

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In early 90's Mandel and coworkers performed an experiment [1] to examine the significance of quantum phase operators by measuring the phase between two optical fields. We show that this type of quantum mechanical phase measurement is possible for matter-waves of ultracold atoms in a double well. In the limit of low number of atoms quantum and classical phases are drastically different. However, in the large particle number limit, they are quite similar. We assert that the matter-wave counterpart of the experiment [1] is realizable with the evolving technology of atom optics .

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Section: Phase-operators: a Brief Reviewmentioning

confidence: 99%

Section: Phase-operators: a Brief Reviewmentioning

confidence: 99%

“…Both of them are canonically conjugate to the number-difference operator. These two phase operators plus the numberdifference operator forms a closed algebra [4].…”

Section: Phase-operators: a Brief Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Matter-wave phase operators for quantum atom optics: On the possibility of experimental verification

Adhikary,

Mal,

Saha

et al. 2021

Preprint

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“…In terms of number and quantum phase variables, the number and phase squeezing properties are also different in two cases [26]. Quantum phase fluctuations are calculated using the recently introduced quantum mechanical phase operators for matter-waves [27].…”

Section: Introductionmentioning

confidence: 99%

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

Mal¹,

Adhikary²,

Deb³

2019

J. Phys. B: At. Mol. Opt. Phys.

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In a recent work, Murmann et. al. [Phys. Rev. Lett. 114, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two spin components. We first discuss building up the Hubbard models using the model finite-range interaction potentials of Jost and Kohn. In general, a finite range of interaction leads to on-site, inter-site, exchange and partial-exchange terms. We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single-and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both fermionic and bosonic cases. But, quantum entanglement and quantum fluctuations are found to be markedly different for the two cases. We discuss atom-atom entanglement in two spatial modes corresponding to the two sites of the double-well. Our results show that the entanglement of a pair of spin-half fermions is always greater than that of spinless bosons; and when the fermions are maximally entangled the fluctuation in the two-mode phase difference is largely squeezed. In contrast, spinless bosons never exhibit phase squeezing, but shows squeezing in two-mode population imbalance depending on the system parameters.

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Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential

Adhikary

Mal

Deb

et al. 2018

J. Phys. B: At. Mol. Opt. Phys.

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Abstract.In a previous paper [Das B et al. J. Phys. B: At. Mol. Opt. Phys 2013 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 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. Twomode 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-one dimensional double-well (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 phase 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.Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and lar

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Unitary quantum phase operators for bosons and fermions: a model study on the quantum phases of interacting particles in a symmetric double-well potential

Cited by 4 publications

References 45 publications

Matter-wave phase operators for quantum atom optics: On the possibility of experimental verification

Matter-wave phase operators for quantum atom optics: On the possibility of experimental verification

Fermionic versus bosonic two-site Hubbard models with a pair of interacting cold atoms

Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential

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