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, Kingshuk; Mal, Subhanka; Deb, Bimalendu; Das, Biswajit; Dastidar, Krishna Rai; Gupta, Subhasish Dutta

doi:10.1088/1361-6455/aaa31c

Cited by 4 publications

(8 citation statements)

References 73 publications

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“…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%

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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%

“…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%

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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“…lr corresponding to the cosine and sine, respectively, of the phase-difference between the left and right modes of the fermions (a ≡ F ) or bosons (a = B). These two operators do not commute with the population imbalance operator Ŵ = Nl − Nr where Nj = â † j âj for spinless bosons or Nj = σ=↑,↓ â † jσ âjσ for two-component fermions or bosons, leading to number-phase uncertainty relations [26]. It is theoretically shown that, these quantum phase operators are particularly important for matter-waves with low number of bosons or fermions, consistent with the similar result in case of photons as shown in [42].…”

Section: Entanglementmentioning

confidence: 99%

“…However, the properties of quantum entanglement and quantum fluctuations are found to be markedly different for a pair of spin-half fermions vis-a-vis a pair of spinless bosons. 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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“…Under tightbinding 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. We defined the standard quantum limit (SQL) for phase and number fluctuations and described two-mode squeezing for number and phase variables for this system [32].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of dipolar Atom-Molecular BEC in a double well potential: Effect of atom-molecular coherent coupling

Dastidar,

Gupta

2021

Preprint

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In the present work we have studied the dynamics of dipolar atommolecular Bose Einstein Condensates coupled via Feshbach Resonance in a double well potential. We have numerically solved four coupled GP like equations, two for left well and two for right well for this atom molecular coupled system. Our numerical results show that both the long-range dipole-dipole interaction (chosen to be positive) and the coherent coupling interaction (which is positive for bosons) facilitate the transmission of atoms and molecules from left well to the right well when the population in the right well dominates over that in the left well and is trapped for a period of time. Whereas in absence of any one of these interactions probability of transient transmission decreases. However in absence of both the interactions (dipole-dipole and coherent coupling) i.e. when only the repulsive contact interaction is present, it leads to self trapping in the left well for a period of time. It is also shown that the signature of coherent coupling between atoms and molecules on the density distribution of atoms in the double well potential is present both in absence and presence of dipole-dipole interaction.

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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

Cited by 4 publications

References 73 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

Dynamics of dipolar Atom-Molecular BEC in a double well potential: Effect of atom-molecular coherent coupling

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