Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1208.0173 · Journal of Physics B Atomic Molecular and Optical Physics

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

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

Published Jan 11, 2013• 1 citation
arXivHTMLPDF

Abstract

We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators and compare the results for different number of bosons. We find that the results for unitary quantum phase operators are significantly different from those for non-unitary ones especially in the case of low number of bosons. We introduce unitary operators corresponding to the quantum phase-difference between two single-particle states of fermions. As an application of fermionic phase operators, we study a simple model of a pair of interacting two-component fermions in a symmetric double-well potential. We also investigate quantum phase and number fluctuations to ascertain number-phase uncertainty in terms of unitary phase operators.

DOI
10.1088/0953-4075/46/3/035501

Related papers

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

Kingshuk Adhikary, Subhanka Mal, Bimalendu Deb +3 more

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.

arXiv:1710.03597•Journal of Physics B Atomic Molecular and Optical Physics•Dec 20, 2017•4 citations

Tunneling dynamics and phase transition of a Bose-Fermi mixture in a double well

Qi Peng-Tang, Wen‐Shan Duan

The coherent nonlinear tunneling dynamics of a boson-fermion mixture in a double-well potential is studied in this paper. Four types of phase are found for the mixture. The first one is two species localizing in different potential wells. The second one is two species coexisting in the same well. The third one is two species equally populated in two wells. The fourth one is one species equally populated in two wells while the other species is in one well. The phase transitions among these four states have been investigated. The interspecies and intraspecies interactions as well as bosonic and fermionic numbers can dramatically affect these phase transitions.

Physical Review A•Sep 22, 2011•18 citations

Phase operators and a special kind of transformation in the Hilbert space of a two-mode boson

Sixia Yu

A special kind of unitary transformation capable of changing the degrees of freedom of a quantum system, a super quantum coordinate transformation, is introduced. Two such transformations in the Hilbert space of a two-mode boson are investigated in detail. Under one transformation, this two-mode bosonic Hilbert space is transformed to a Hilbert space of a two-mode boson plus a single-mode fermion; under the other transformation, it is transformed to a Hilbert space of a single-mode boson. Their applications to phase operators and the phase difference operator are discussed.

Physical Review A•Nov 1, 1997•6 citations

Operators

FRANCESCO IACHELLO, P. Van Isacker

Introduction In many cases in physics, one has to deal simultaneously with collective and single-particle excitations of the system. The collective excitations are usually bosonic in nature while the single-particle excitations are often fermionic. One is therefore led to consider a system which includes bosons and fermions. In this book we discuss applications of a general algebraic theory of mixed Bose- Fermi systems to atomic nuclei. The collective degrees of freedom here can be described in terms of a system of interacting bosons as discussed in a previous book (Iachello and Arima, 1987), henceforth referred to as Volume 1. The single-particle degrees of freedom represent the motion of individual nucleons in the average nuclear field. They are described in terms of a system of interacting fermions. The coupling of fermions and bosons leads to the interacting boson-fermion model which has been used extensively in recent years to discuss the properties of nuclei with an odd number of nucleons. The interacting boson-fermion model was introduced by Arima and one of us in 1975 (Arima and Iachello, 1975). It was subsequently expanded by Iachello and Scholten (1979) and cast into a form more readily amenable to calculations. As in the corresponding case of even-mass systems, the algebra of creation and annihilation operators can be realized in several ways. One of these is the Hoistein-Primakoff realization which leads to a slightly different version of the interacting boson-fermion model called the truncated quadrupole phonon-fermion model (Paar, 1980; Paar and Brant, 1981), based on the boson realization introduced by Janssen, Jolos and Donau in 1974 and discussed in Sect. 1.4.6 of Volume 1.

Cambridge University Press eBooks•Aug 30, 1991•0 citations

Quantum particle-number fluctuations in a two-component Bose gas in a double-well potential

Paweł Zin, Bartłomiej Oleś, Krzysztof Sacha

A two-component Bose gas in a double-well potential with repulsive interactions may undergo a phase separation transition if the interspecies interactions outweigh the intraspecies ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components; that is, the probability for observation of any mixture of particles in each potential well becomes uniform.

arXiv:1004.1541•Physical Review A•Sep 14, 2011•8 citations

Interacting bosons in a double-well potential : localization regime

Nicolas Rougerie, Dominique Spehner

We study the ground state of a large bosonic system trapped in a symmetric double-well potential, letting the distance between the two wells increase to infinity with the number of particles. In this context, one should expect an interaction-driven transition between a delocalized state (particles are independent and all live in both wells) and a localized state (particles are correlated, half of them live in each well). We start from the full many-body Schr{ö}dinger Hamiltonian in a large-filling situation where the on-site interaction and kinetic energies are comparable. When tunneling is negligible against interaction energy, we prove a localization estimate showing that the particle number fluctuations in each well are strongly suppressed. The modes in which the particles condense are minimizers of nonlinear Schr{ö}dinger-type functionals.

arXiv:1612.05758•Dec 17, 2016•0 citations
We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators and compare the results for different number of bosons. We find that the results for unitary quantum phase operators are significantly different from those for non-unitary ones especially in the case of low number of bosons. We introduce unitary operators corresponding to the quantum phase-difference between two single-particle states of fermions. As an application of fermionic phase operators, we study a simple model of a pair of interacting two-component fermions in a symmetric double-well potential. We also investigate quantum phase and number fluctuations to ascertain number-phase uncertainty in terms of unitary phase operators.
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.
The coherent nonlinear tunneling dynamics of a boson-fermion mixture in a double-well potential is studied in this paper. Four types of phase are found for the mixture. The first one is two species localizing in different potential wells. The second one is two species coexisting in the same well. The third one is two species equally populated in two wells. The fourth one is one species equally populated in two wells while the other species is in one well. The phase transitions among these four states have been investigated. The interspecies and intraspecies interactions as well as bosonic and fermionic numbers can dramatically affect these phase transitions.
A special kind of unitary transformation capable of changing the degrees of freedom of a quantum system, a super quantum coordinate transformation, is introduced. Two such transformations in the Hilbert space of a two-mode boson are investigated in detail. Under one transformation, this two-mode bosonic Hilbert space is transformed to a Hilbert space of a two-mode boson plus a single-mode fermion; under the other transformation, it is transformed to a Hilbert space of a single-mode boson. Their applications to phase operators and the phase difference operator are discussed.
Introduction In many cases in physics, one has to deal simultaneously with collective and single-particle excitations of the system. The collective excitations are usually bosonic in nature while the single-particle excitations are often fermionic. One is therefore led to consider a system which includes bosons and fermions. In this book we discuss applications of a general algebraic theory of mixed Bose- Fermi systems to atomic nuclei. The collective degrees of freedom here can be described in terms of a system of interacting bosons as discussed in a previous book (Iachello and Arima, 1987), henceforth referred to as Volume 1. The single-particle degrees of freedom represent the motion of individual nucleons in the average nuclear field. They are described in terms of a system of interacting fermions. The coupling of fermions and bosons leads to the interacting boson-fermion model which has been used extensively in recent years to discuss the properties of nuclei with an odd number of nucleons. The interacting boson-fermion model was introduced by Arima and one of us in 1975 (Arima and Iachello, 1975). It was subsequently expanded by Iachello and Scholten (1979) and cast into a form more readily amenable to calculations. As in the corresponding case of even-mass systems, the algebra of creation and annihilation operators can be realized in several ways. One of these is the Hoistein-Primakoff realization which leads to a slightly different version of the interacting boson-fermion model called the truncated quadrupole phonon-fermion model (Paar, 1980; Paar and Brant, 1981), based on the boson realization introduced by Janssen, Jolos and Donau in 1974 and discussed in Sect. 1.4.6 of Volume 1.
A two-component Bose gas in a double-well potential with repulsive interactions may undergo a phase separation transition if the interspecies interactions outweigh the intraspecies ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components; that is, the probability for observation of any mixture of particles in each potential well becomes uniform.
We study the ground state of a large bosonic system trapped in a symmetric double-well potential, letting the distance between the two wells increase to infinity with the number of particles. In this context, one should expect an interaction-driven transition between a delocalized state (particles are independent and all live in both wells) and a localized state (particles are correlated, half of them live in each well). We start from the full many-body Schr{ö}dinger Hamiltonian in a large-filling situation where the on-site interaction and kinetic energies are comparable. When tunneling is negligible against interaction energy, we prove a localization estimate showing that the particle number fluctuations in each well are strongly suppressed. The modes in which the particles condense are minimizers of nonlinear Schr{ö}dinger-type functionals.