Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space

Patra, Pinaki

doi:10.1007/s11128-022-03776-3

Cited by 4 publications

(1 citation statement)

References 61 publications

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“…It is almost a Gospel that the fundamental concept of space-time is mostly compatible with quantum theory in NC-space [26,27]. Therefore, extending ideas of the commutative space quantum mechanics to noncommutative (NC)-space is always an interesting aspect in its own right [28][29][30][31][32][33][34]. In this paper, we study entanglement between coordinate degrees of freedom induced by both the position-position and momentum-momentum noncommutativity parameters, as well as the anisotropy due to the mass and frequency of a quantum mechanical oscillator.…”

Section: Introductionmentioning

confidence: 99%

Squeezed coherent states for gravitational well in noncommutative space

Patra¹,

Saha

Biswas

2021

Indian J Phys

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Gravitational well is a widely used system for the verification of the quantum weak equivalence principle (WEP). We have studied the quantum gravitational well (GW) under the shed of non-commutative (NC) space so that the results can be utilized for testing the validity of WEP in NC-space. To keep our study widely usable, we have considered both position-position and momentum-momentum non-commutativity. Since coherent state (CS) structure provides a natural bridge between the classical and quantum domain descriptions, the quantum domain validity of purely classical phenomena like free-fall under gravity might be verified with the help of CS. We have constructed CS with the aid of a Lewis-Riesenfeld phase space invariant operator. We deduced the uncertainty relations from the expectation values of the observables and shown that the solutions of the time-dependent Schrödinger equation are squeezed-coherent states.

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Section: Introductionmentioning

confidence: 99%

Squeezed coherent states for gravitational well in noncommutative space

Patra¹,

Saha

Biswas

2021

Indian J Phys

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On the $$\mathcal {P}\mathcal {T}$$-Symmetric Parametric Amplifier

Patra

2023

Braz J Phys

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Tuning the separability in noncommutative space

Patra

2024

Journal of Mathematical Physics

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With the help of the generalized Peres–Horodecki separability criterion (Simon’s condition) for a bipartite Gaussian state, we have studied the separability of the noncommutative (NC) space coordinate degrees of freedom. Non-symplectic nature of the transformation between the usual commutative space and NC space restricts the straightforward use of Simon’s condition in NCS. We have transformed the NCS system to an equivalent Hamiltonian in commutative space through the Bopp shift, which enables the utilization of the separability criterion. To make our study fairly general and to analyze the effect of parameters on the separability of bipartite state in NC-space, we have considered a bilinear Hamiltonian with time-dependent (TD) parameters, along with a TD external interaction, which is linear in field modes. The system is transformed (Sp(4,R)) into canonical form keeping the intrinsic symplectic structure intact. The solution of the TD-Schrödinger equation is obtained with the help of the Lewis–Riesenfeld invariant method (LRIM). Expectation values of the observables (thus the covariance matrix) are constructed from the states obtained from LRIM. It turns out that the existence of the NC parameters in the oscillator determines the separability of the states. In particular, for isotropic oscillators, the separability condition for the bipartite Gaussian states depends on specific values of NC parameters. Moreover, particular anisotropic parameter values for the oscillator may cease the separability. In other words, both the deformation parameters (θ, η) and parameter values of the oscillator (mass, frequency) are important characteristics for the separability of bipartite Gaussian states. Thus tuning the parameter values, one can destroy or recreate the separability of states. With the help of a toy model, we have demonstrated how the tuning of a TD-NC space parameter affects the separability.

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Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space

Cited by 4 publications

References 61 publications

Squeezed coherent states for gravitational well in noncommutative space

Squeezed coherent states for gravitational well in noncommutative space

On the $$\mathcal {P}\mathcal {T}$$-Symmetric Parametric Amplifier

Tuning the separability in noncommutative space

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