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

Journal of Physics A Mathematical and Theoretical

New physics in Landau levels

Alireza Dehghani, B. Mojaveri

Published Sep 4, 2013• 16 citations
Publisher

Abstract

The most general displaced number 'coherent' states, based on the Heisenberg, su (2) and su (1, 1) Lie algebras symmetries, are constructed. They depend on two parameters, and can be converted into the well-known photon-added, two variable Glauber coherent states and displaced number states respectively, depending on which of the parameters is equal to zero. The relations of the Weyl–Heisenberg algebra guarantee a corresponding resolution of the identity conditions. A discussion of the statistical properties of these states is included. Significant are their squeezing properties, which can be raised by increasing the energy and angular momentum quantum numbers n and m . The maximum squeezing is obtained for B ext = 0. Depending on the particular choice of parameters in the above scenarios, we are able to determine the status of compliance with Poissonian statistics. In the limiting case, we obtain a major result about the non-classical properties of the Glauber minimum uncertainty coherent states. In other words, in addition to the requirement to minimize uncertainty conditions, they carry non-classical features too. Finally, a theoretical framework is proposed to generate them.

DOI
10.1088/1751-8113/46/38/385303

Related papers

Excited Coherent States Attached to Landau Levels

B. Mojaveri, Alireza Dehghani

A new scheme is proposed to design excited coherent states. where the states $β$,$α$ denote the Glauber two variable minimum uncertainty coherent states, which minimize minimum uncertainty conditions while carrier nonclassical properties too and n is an integer. They are converted into the Agarwal's type of the photon added coherent states, arbitrary Fock states and the Glauber two variable coherent states, respectively depending on which of the parameters $\b{eta}$,$α$ and $n$ equal to zero. It has been shown that the resolution of identity condition is realized with respect to an appropriate measure on the complex plane, too. We have compared our results with the similar quantum states of Agarwal's type and seen that in our case amount of quantum fluctuations are much controllable. Moreover, we have also more flexibility to establish and set-out of their features. Also, there is a discussion on the statistical properties, can unveil (non-)classical properties of these states. For instance their Poissonian statistics are significant similar to what we saw earlier in the Glauber two variable coherent states. Interestingly, depending on the particular choice of the parameters of the above scenarios, we are able to determine the status of compliance with squeezing properties in field quadratures. The last stage is devoted to some theoretical framework to generate them in cavities.

arXiv:1404.5229•Apr 21, 2014•0 citations

The minimum-uncertainty coherent states for Landau levels

Alireza Dehghani, Hossein Fakhri, B. Mojaveri

The Glauber minimum-uncertainty coherent states with two variables for Landau levels, based on the representation of Weyl-Heisenberg algebra by two different modes, have been studied about four decades ago. Here, we introduce new two-variable coherent states with minimum uncertainty relationship for Landau levels in three different methods: the infinite unitary representation of su(1, 1) is realized in two different methods, first, by consecutive levels with the same energy gaps and also with the same value for z-angular momentum quantum number, then, by shifting z-angular momentum mode number by two units while the energy level remaining the same. Besides, for su(2), whether by lowest Landau levels or Landau levels with lowest z-angular momentum, just one finite unitary representation is introduced. Having constructed the generalized Klauder-Perelomov coherent states, for any of the three representations, we obtain their Glauber coherency by displacement operator of Weyl-Heisenberg algebra.

Journal of Mathematical Physics•Dec 1, 2012•22 citations

General displaced SU(1, 1) number states: Revisited

Alireza Dehghani

The most general displaced number states, based on the bosonic and an irreducible representation of the Lie algebra symmetry of su(1, 1) and associated with the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder-Perelomov counterpart, to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime, too, with special nonlinearity functions. They depend on two parameters, and can be converted into the well-known Barut-Girardello coherent and number states, respectively, depending on which of the parameters equal to zero. A discussion of the statistical properties of these states is included. Significant are their squeezing properties and anti-bunching effects which can be raised by increasing the energy quantum number. Depending on the particular choice of the parameters of the above scenario, we are able to determine the status of compliance with flexible statistics. Major parts of the issue is spent on something that these states, in fact, should be considered as new kind of photon-added coherent states, too. Which can be reproduced through an iterated action of a creation operator on new nonlinear Barut-Girardello coherent states. Where the latter carry, also, outstanding statistical features.

arXiv:1404.5219•Journal of Mathematical Physics•Apr 1, 2014•8 citations

SU(1,1) Nonlinear Coherent States

B. Mojaveri, Alireza Dehghani

The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group SU(1, 1). By using of a discrete, unitary and irreducible representation of the Lie algebra su(1, 1) wide range of generalized nonlinear coherent states(GNCS) have been introduced, which admit a resolution of the identity through positive definite measures on the complex plane. We have shown that realization of these states for different values of the deformation pa- rameters r = 1 and 2 lead to the well-known Klauder-Perelomov and Barut-Girardello coherent states associated to the Irreps of the Lie algebra su(1, 1), respectively. It is worth to mention that, like the canonical coherent states, GNCS possess the temporal stability property. Finally, studying some statistical characters implies that they have indeed nonclassical features such as squeezing, anti-bunching effect and sub-Poissonian statistics, too.

arXiv:1212.6888•Dec 31, 2012•0 citations

SU(1,1)-displaced coherent states, photon counting, and squeezing

Jean‐Pierre Gazeau, M. A. del Olmo

We revisit the Perelomov SU(1,1)-displaced coherent states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation to photon counting and squeezing. In the non-displaced case, we discuss the efficiency of the photodetector as inversely proportional to the parameterϰof the discrete series of unitary irreducible representations of SU(1,1). In the displaced case, we study the counting and squeezing properties of the states in terms ofϰand the number of photons in the original displaced state. We finally examine the quantization of a classical radiation field based on these families of coherent states. The procedure yields displacement operators that might allow to prepare such states in the way proposed by Glauber for standard coherent states.

arXiv:2304.08031•Journal of the Optical Society of America B•Mar 6, 2023•4 citations

On SU(1,1) intelligent coherent states

G. M. Abd Al-Kader, A.‐S. F. Obada

Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.

Physica Scripta•Aug 22, 2008•3 citations
The most general displaced number 'coherent' states, based on the Heisenberg, su (2) and su (1, 1) Lie algebras symmetries, are constructed. They depend on two parameters, and can be converted into the well-known photon-added, two variable Glauber coherent states and displaced number states respectively, depending on which of the parameters is equal to zero. The relations of the Weyl–Heisenberg algebra guarantee a corresponding resolution of the identity conditions. A discussion of the statistical properties of these states is included. Significant are their squeezing properties, which can be raised by increasing the energy and angular momentum quantum numbers n and m . The maximum squeezing is obtained for B ext = 0. Depending on the particular choice of parameters in the above scenarios, we are able to determine the status of compliance with Poissonian statistics. In the limiting case, we obtain a major result about the non-classical properties of the Glauber minimum uncertainty coherent states. In other words, in addition to the requirement to minimize uncertainty conditions, they carry non-classical features too. Finally, a theoretical framework is proposed to generate them.
A new scheme is proposed to design excited coherent states. where the states βββ,ααα denote the Glauber two variable minimum uncertainty coherent states, which minimize minimum uncertainty conditions while carrier nonclassical properties too and n is an integer. They are converted into the Agarwal's type of the photon added coherent states, arbitrary Fock states and the Glauber two variable coherent states, respectively depending on which of the parameters $\b{eta}$,ααα and nnn equal to zero. It has been shown that the resolution of identity condition is realized with respect to an appropriate measure on the complex plane, too. We have compared our results with the similar quantum states of Agarwal's type and seen that in our case amount of quantum fluctuations are much controllable. Moreover, we have also more flexibility to establish and set-out of their features. Also, there is a discussion on the statistical properties, can unveil (non-)classical properties of these states. For instance their Poissonian statistics are significant similar to what we saw earlier in the Glauber two variable coherent states. Interestingly, depending on the particular choice of the parameters of the above scenarios, we are able to determine the status of compliance with squeezing properties in field quadratures. The last stage is devoted to some theoretical framework to generate them in cavities.
The Glauber minimum-uncertainty coherent states with two variables for Landau levels, based on the representation of Weyl-Heisenberg algebra by two different modes, have been studied about four decades ago. Here, we introduce new two-variable coherent states with minimum uncertainty relationship for Landau levels in three different methods: the infinite unitary representation of su(1, 1) is realized in two different methods, first, by consecutive levels with the same energy gaps and also with the same value for z-angular momentum quantum number, then, by shifting z-angular momentum mode number by two units while the energy level remaining the same. Besides, for su(2), whether by lowest Landau levels or Landau levels with lowest z-angular momentum, just one finite unitary representation is introduced. Having constructed the generalized Klauder-Perelomov coherent states, for any of the three representations, we obtain their Glauber coherency by displacement operator of Weyl-Heisenberg algebra.
The most general displaced number states, based on the bosonic and an irreducible representation of the Lie algebra symmetry of su(1, 1) and associated with the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder-Perelomov counterpart, to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime, too, with special nonlinearity functions. They depend on two parameters, and can be converted into the well-known Barut-Girardello coherent and number states, respectively, depending on which of the parameters equal to zero. A discussion of the statistical properties of these states is included. Significant are their squeezing properties and anti-bunching effects which can be raised by increasing the energy quantum number. Depending on the particular choice of the parameters of the above scenario, we are able to determine the status of compliance with flexible statistics. Major parts of the issue is spent on something that these states, in fact, should be considered as new kind of photon-added coherent states, too. Which can be reproduced through an iterated action of a creation operator on new nonlinear Barut-Girardello coherent states. Where the latter carry, also, outstanding statistical features.
The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group SU(1, 1). By using of a discrete, unitary and irreducible representation of the Lie algebra su(1, 1) wide range of generalized nonlinear coherent states(GNCS) have been introduced, which admit a resolution of the identity through positive definite measures on the complex plane. We have shown that realization of these states for different values of the deformation pa- rameters r = 1 and 2 lead to the well-known Klauder-Perelomov and Barut-Girardello coherent states associated to the Irreps of the Lie algebra su(1, 1), respectively. It is worth to mention that, like the canonical coherent states, GNCS possess the temporal stability property. Finally, studying some statistical characters implies that they have indeed nonclassical features such as squeezing, anti-bunching effect and sub-Poissonian statistics, too.
We revisit the Perelomov SU(1,1)-displaced coherent states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation to photon counting and squeezing. In the non-displaced case, we discuss the efficiency of the photodetector as inversely proportional to the parameterϰof the discrete series of unitary irreducible representations of SU(1,1). In the displaced case, we study the counting and squeezing properties of the states in terms ofϰand the number of photons in the original displaced state. We finally examine the quantization of a classical radiation field based on these families of coherent states. The procedure yields displacement operators that might allow to prepare such states in the way proposed by Glauber for standard coherent states.
Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.