Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations

Dey, Sanjib; Hussin, Véronique

doi:10.1103/physrevd.91.124017

Cited by 49 publications

(68 citation statements)

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“…In this article, we propose yet another alternative way to obtain a squeezed atom laser by using a model, which not only has a strong mathematical ground originating from the quantum group, but also it demonstrates ample interesting results in generating squeezed states and in other aspects of quantum optics [21][22][23][24][25]. Previously, it was shown that the optical squeezing properties are inherited in these models by construction, here we show that it is true for the atom laser case also.…”

Section: Squeezed Atom Laser For Bec With Minimal Lengthmentioning

confidence: 58%

“…The corresponding observables X and P are represented in terms of the usual canonical variables x, p satisfying [x, p] = i . The model (2.1) has been explored extensively to construct coherent states, squeezed states, etc., as well as their physical implications have been discussed [22,23,25]. One interesting aspect of such model is that it can be associated with standard nonlinear generalized models by using some mathematical techniques.…”

Section: Minimal Length and Generalised Uncertainty Principlementioning

confidence: 99%

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Squeezed Atom Laser for Bose-Einstein Condensate with Minimal Length

Dey

Hussin

2019

Int J Theor Phys

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We study a protocol for constructing a squeezed atom laser for a model originating from the generalized uncertainty principle. We show that the squeezing effects arising from such systems do not require any squeezed light as an input, but the squeezing appears automatically because of the structure of the model it owns. The output atom laser beam becomes squeezed due to the nonlinear interaction between the Bose-Einstein condensate and the deformed radiation field created due to the noncommutative structure. We analyze several standard squeezing techniques based on the analytical expressions followed by a numerical analysis for further insights.

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Section: Squeezed Atom Laser For Bec With Minimal Lengthmentioning

confidence: 58%

Section: Minimal Length and Generalised Uncertainty Principlementioning

confidence: 99%

Squeezed Atom Laser for Bose-Einstein Condensate with Minimal Length

Dey

Hussin

2019

Int J Theor Phys

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“…Enhancement of entanglement in non-commutative space has been explored in details [52]. This raises a question whether deformed space structure can give a boost to the quantum engines under study.…”

Section: Discussionmentioning

confidence: 99%

Relativistic quantum heat engine from uncertainty relation standpoint

Chattopadhyay

Paul

2019

Sci Rep

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Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

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“…Other interesting structures exist in the literature which leads to instances like minimal length and generalized version of Heisenberg's uncertainty relations. These are obtained when θ µν is considered to be a function of the coordinates and momenta [4,5].…”

Section: Introductionmentioning

confidence: 99%

Non-commutative space: boon or bane for quantum engines and refrigerators

Chattopadhyay

2020

Eur. Phys. J. Plus

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Various quantum systems are considered as the working substance for the analysis of quantum heat cycles and quantum refrigerators. For example, one can consider harmonic oscillator as a working substance for the Carnot cycle to evaluate the efficiency and work of the engine. Even one can explore the coefficient of performance for the refrigerators by implementing a harmonic oscillator as a working substance for different cycles. However, for all these methods the efficiency of the engines cannot exceed the Carnot efficiency. So, a question arises whether a change in the space structure can provide any boost for the quantum engines and the refrigerators. Here, in this paper, we have studied the efficiency of the heat engine cycle and the coefficient of performance of the refrigerator cycles in the non-commutative space. The efficiency of the quantum heat engines gets a boost with the change in the space structure than the traditional quantum heat engine but the effectiveness of the noncommutative parameter is less for the efficiency compared to the coefficient of performance of the refrigerator. There is a steep boost for the coefficient of performance of the refrigerator cycles for the non-commutative space a harmonic oscillator compared to the harmonic oscillator.

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Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations

Cited by 49 publications

References 50 publications

Squeezed Atom Laser for Bose-Einstein Condensate with Minimal Length

Squeezed Atom Laser for Bose-Einstein Condensate with Minimal Length

Relativistic quantum heat engine from uncertainty relation standpoint

Non-commutative space: boon or bane for quantum engines and refrigerators

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