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

Physical Review A

Cooperative behavior of atoms irradiated by broadband squeezed light

G. S. Agarwal, Ravinder Rupchand Puri

Published Apr 1, 1990• 200 citations
Publisher

Abstract

We consider the dynamics of a collection of atoms interacting with a coherent field and a broadband squeezed vacuum. We obtain an exact solution of the master equation and study in detail the types of nonequilibrium steady states that can be generated. We show that in the absence of coherent drive the atoms are in a state whose properties are similar to those of the squeezed vacuum for photons. We demonstrate that the steady state for certain discrete values of the external field strength and detuning is a pure state which is the eigenstate of the non-Hermitian operator cosh(\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert})${\mathit{S}}^{\mathrm{\ensuremath{-}}}$+sinh(\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert})${\mathit{S}}^{+}$, where \ensuremath{\xi} is the squeezing parameter associated with the input radiation field. These eigenstates play a very fundamental role in the theory and satisfy the equality sign in the Heisenberg uncertainty relation \ensuremath{\Delta}${\mathit{S}}_{\mathit{x}}$ \ensuremath{\Delta}${\mathit{S}}_{\mathit{y}}$\ensuremath{\ge}1/2\ensuremath{\Vert}〈${\mathit{S}}_{\mathit{z}}$〉\ensuremath{\Vert}. We also present detailed numerical results for the characteristics of the field generated by the collective system.

DOI
10.1103/physreva.41.3782

Related papers

Nonequilibrium phase transitions in a squeezed cavity generation of spin states satisfying the Heisenberg uncertainty equality

G. S. Agarwal, Ravinder Rupchand Puri

We investigate the cooperative and phase transition behavior of the coherently driven system, which in addition is interacting with a broadband squeezed radiation. We obtain an exact steady state solution of the master equation in the form where Ω0 = (µΩ − νΩ*)/Γ and N is determined from normalization.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Coherently driven two-level atom coupled to a broadband squeezed vacuum

Sintayehu Tesfa

We analyse the effects of the external coherent radiation and squeezed input on a two-level atom placed in a cavity applying the corresponding master equation. We study the atomic dynamics as well as the squeezing and statistical properties of the cavity radiation by analytically solving the associated differential equations. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent and squeezed input. However, a strong external coherent radiation splits the line of the emission spectrum, whereas the squeezing broadens the width and significantly decreases the height of the spectrum. It is also found that the emitted radiation exhibits photon anti-bunching, super-Poissonian photon statistics and squeezing.

Journal of Modern Optics•Aug 15, 2007•14 citations

Generation of atomic-squeezed states in an optical cavity with an injected squeezed vacuum

Arup Banerjee

We study the generation of atomic-squeezed states in an optical cavity. The cavity encloses a pair of two-level atoms and is coupled to a broadband squeezed vacuum. Using the bad-cavity limit, cavity field is adiabatically eliminated to obtain the equations of motion for collective atomic operators. These equations are then employed to obtain the atomic density-matrix elements and to study the generation of atomic-squeezed states in the steady state. To characterize atomic-squeezed states we use the squeezing parameter defined recently by Wineland et al. [Phys. Rev. A 46, 6797 (1992)] for spectroscopic purposes. The aforementioned parameter is also compared with the squeezing parameter obtained from the uncertainty principle satisfied by the collective atomic operators. We show that in a cavity arrangement, unlike free space, atomic-squeezed states can be generated only for a restricted range of values of the parameters \ensuremath{\lambda} and N which characterize the cavity and the squeezed field driving the cavity, respectively. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Dec 1, 1996•13 citations

Phase-sensitive population decay: The two-atom Dicke model in a broadband squeezed vacuum

G. Massimo Palma, P. L. Knight

We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.

Physical Review A•Feb 1, 1989•112 citations

Two photon cooperative absorption and radiation of nonclassical light

N. A. Enaki

The present report deals with the condition under which an ensemble of atoms goes over into a regime of collective two-photon nutation, and with the behavior of Rabi frequency as function of external light. To simplify this problem, we consider a system of Λ-type atoms that enters into two-photon resonance with an external squeezed electromagnetic field relative to the forbidden transition ∣1> ∣2> , where ∣1> and ∣2> are ground and first exited states [1,2] The situation is examining, when the values of quantum fluctuations of electromagnetic field intensity have the same value as the mean value of electromagnetic field intensity. This is one of main difference between the our paper and [2]. The proposed mathematical model permits to take into account all the two-photon diagrams. These diagrams describe not only resonance two-photon transitions but two-photon scattering processes between ∣1> and ∣2> levels too. Using mathematical method which is proposed in [1,2] it is obtained the master equation for the atom subsystem. Two stationary solutions for the case when Rabi frequency is larger than the inverse value of the collective two-photon decay time and the case when external light is coherent are examined. It is showing that the absorption rate of an phase squeezed field is larger than the absorption rate of an amplitude squeezed light. We also obtained the behavior of inversion between the levels ∣1> and ∣2>, when the collective of atoms enters into two-photon resonance with external field.

17th Congress of the International Commission for Optics: Optics for Science and New Technology•Sep 1, 1996•0 citations

Photon Absorptions of a Driven Three-Level Atom in a Squeezed Vacuum

Zhaoyang Chen, Yan Xu, Zhi‐Cheng Wang

A three-level ladder atom driven by two coherent laser fields with rather different frequencies in various kinds of reservoirs is considered. Making use of the master equation and Bloch equation, we calculate numerically and show graphically the steady-state populations versus two-photon detuning. We also discuss and compare the two-photon and one-photon processes occurring for various cases. For a squeezed vacuum, only when the carrier frequency of the squeezed vacuum equals the average of frequencies of the two driving fields and the phase matching condition is fulfilled, will there be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field; Otherwise, the two-photon ab-sorption rate from the squeezed vacuum will be greatly diminished.

Journal of the Physical Society of Japan•Aug 15, 1998•0 citations
We consider the dynamics of a collection of atoms interacting with a coherent field and a broadband squeezed vacuum. We obtain an exact solution of the master equation and study in detail the types of nonequilibrium steady states that can be generated. We show that in the absence of coherent drive the atoms are in a state whose properties are similar to those of the squeezed vacuum for photons. We demonstrate that the steady state for certain discrete values of the external field strength and detuning is a pure state which is the eigenstate of the non-Hermitian operator cosh(\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert})S\ensuremath−{\mathit{S}}^{\mathrm{\ensuremath{-}}}S\ensuremath−+sinh(\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert})S+{\mathit{S}}^{+}S+, where \ensuremath{\xi} is the squeezing parameter associated with the input radiation field. These eigenstates play a very fundamental role in the theory and satisfy the equality sign in the Heisenberg uncertainty relation \ensuremath{\Delta}Sx{\mathit{S}}_{\mathit{x}}Sx​ \ensuremath{\Delta}Sy{\mathit{S}}_{\mathit{y}}Sy​\ensuremath{\ge}1/2\ensuremath{\Vert}〈Sz{\mathit{S}}_{\mathit{z}}Sz​〉\ensuremath{\Vert}. We also present detailed numerical results for the characteristics of the field generated by the collective system.
We analyse the effects of the external coherent radiation and squeezed input on a two-level atom placed in a cavity applying the corresponding master equation. We study the atomic dynamics as well as the squeezing and statistical properties of the cavity radiation by analytically solving the associated differential equations. It is found that the atom stays in the lower energy level more often at steady state irrespective of the strength of the coherent and squeezed input. However, a strong external coherent radiation splits the line of the emission spectrum, whereas the squeezing broadens the width and significantly decreases the height of the spectrum. It is also found that the emitted radiation exhibits photon anti-bunching, super-Poissonian photon statistics and squeezing.
We study the generation of atomic-squeezed states in an optical cavity. The cavity encloses a pair of two-level atoms and is coupled to a broadband squeezed vacuum. Using the bad-cavity limit, cavity field is adiabatically eliminated to obtain the equations of motion for collective atomic operators. These equations are then employed to obtain the atomic density-matrix elements and to study the generation of atomic-squeezed states in the steady state. To characterize atomic-squeezed states we use the squeezing parameter defined recently by Wineland et al. [Phys. Rev. A 46, 6797 (1992)] for spectroscopic purposes. The aforementioned parameter is also compared with the squeezing parameter obtained from the uncertainty principle satisfied by the collective atomic operators. We show that in a cavity arrangement, unlike free space, atomic-squeezed states can be generated only for a restricted range of values of the parameters \ensuremath{\lambda} and N which characterize the cavity and the squeezed field driving the cavity, respectively. \textcopyright{} 1996 The American Physical Society.
We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.
The present report deals with the condition under which an ensemble of atoms goes over into a regime of collective two-photon nutation, and with the behavior of Rabi frequency as function of external light. To simplify this problem, we consider a system of Λ-type atoms that enters into two-photon resonance with an external squeezed electromagnetic field relative to the forbidden transition ∣1> ∣2> , where ∣1> and ∣2> are ground and first exited states [1,2] The situation is examining, when the values of quantum fluctuations of electromagnetic field intensity have the same value as the mean value of electromagnetic field intensity. This is one of main difference between the our paper and [2]. The proposed mathematical model permits to take into account all the two-photon diagrams. These diagrams describe not only resonance two-photon transitions but two-photon scattering processes between ∣1> and ∣2> levels too. Using mathematical method which is proposed in [1,2] it is obtained the master equation for the atom subsystem. Two stationary solutions for the case when Rabi frequency is larger than the inverse value of the collective two-photon decay time and the case when external light is coherent are examined. It is showing that the absorption rate of an phase squeezed field is larger than the absorption rate of an amplitude squeezed light. We also obtained the behavior of inversion between the levels ∣1> and ∣2>, when the collective of atoms enters into two-photon resonance with external field.
A three-level ladder atom driven by two coherent laser fields with rather different frequencies in various kinds of reservoirs is considered. Making use of the master equation and Bloch equation, we calculate numerically and show graphically the steady-state populations versus two-photon detuning. We also discuss and compare the two-photon and one-photon processes occurring for various cases. For a squeezed vacuum, only when the carrier frequency of the squeezed vacuum equals the average of frequencies of the two driving fields and the phase matching condition is fulfilled, will there be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field; Otherwise, the two-photon ab-sorption rate from the squeezed vacuum will be greatly diminished.