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

Squeezed-state generation in a spatially varying field mode without adiabatic elimination

D. M. Hope, David E. McClelland, Craig M. Savage

Published May 1, 1990• 8 citations
Publisher

Abstract

We investigate the effect of a spatially varying field mode on the squeezing generated by two-level atoms interacting with a single mode of an optical cavity. The mode structure is incorporated into a quantum theory that does not employ adiabatic elimination of field or atomic variables. Thus we are able to consider the regime in which cavity and atomic decay rates are approximately equal as well as the good- and bad-cavity limits. Calculations show that squeezing is reduced by the inclusion of a Gaussian transverse mode profile and a standing-wave structure for a particular value of atomic cooperativity C. The model is consistent with recent measurements of squeezing. The degree of squeezing reduction depends on the ratio of cavity and atomic damping rates, in the regime where they are similar in size.

DOI
10.1103/physreva.41.5074

Related papers

Squeezed-state generation for two-level atoms in a spatially varying field mode

Min Xiao, H. J. Carmichael, H. J. Kimble

A spatially varying field mode is included in calculating the squeezing effect for a system of two-level atoms in the good-cavity limit. Two examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are used to demonstrate the quite general method. In qualitative terms, the squeezing predicted for plane waves is preserved. However, for a given value of atomic cooperativity parameter C, there is a degradation in squeezing because of the spatially varying field structure.

Journal of the Optical Society of America B•Oct 1, 1987•8 citations

Squeezed slate generation for two-level atoms in a spatially varying field mode

Min Xiao, H. Jeffrey Kimble, H. J. Carmichael

Squeezed state generation for a system of two-level atoms interacting with the field of a high-finesse cavity has been extensively discussed both experimentally and theoretically in recent years. Most theories describing these systems take the cavity field as a plane traveling wave for simplicity. With this assumption it is quite difficult to make quantitative comparisons between theory and recent experiments. However, by employing the formalism developed in Ref. 1, we are able to treat rather general spatial variations of the intracavity field subject to the constraint of the good-cavity limit of optical bistability. Squeezed state generation for the three particular examples of a plane-wave ring interferometer, a Gaussian-mode ring cavity, and a plane-wave field in a standing-wave interferometer are considered to illustrate the formalism. Somewhat surprisingly, in regimes for which the plane-wave theory predicts 50-70% squeezing (cooperatively C ~102–103), the standing-wave structure produces only modest reductions in the squeezing (a few percent), while the radial variations of the field reduce the squeezing by ~10%.

Annual Meeting Optical Society of America•Jan 1, 1987•0 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

Theory of intracavity atom-field interactions with squeezed inputs

T. A. B. Kennedy, Daniel F. Walls

We give a general theory of the interaction of a large number of two-level atoms in an optical cavity driven by a broadband squeezed input of finite amplitude. No adiabatic elimination of atoms or field is made, and atomic and cavity loss and dispersion are fully incorporated in the theory. We calculate the optical and squeezing spectra that may be observed in transmission and reflection from the cavity; the latter exhibits a novel interference structure superimposed as a result of the squeezed input. Results presented indicate that it is possible to somewhat reduce the vacuum Rabi peaks in transmission, in the strong-coupling regime, with a moderately squeezed input. In the limit of a ``bad cavity,'' the characteristic triplet transmitted under conditions of saturation may have one of its sidebands suppressed and the other enhanced by a squeezed input. These signatures suggest new alternatives for the experimental study of the interaction of atoms with squeezed light.

Physical Review A•Sep 1, 1990•17 citations

Squeezing with coupled pendulums: two-level atoms in a cavity

Mark G. Raizen, Luis A. Orozco, Min Xiao +2 more

A theoretical and experimental investigation of the generation of squeezed states of light has been carried out for a system of two-level atoms inside a high-finesse cavity. The regime that we consider is such that the coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom-field system (the so-called vacuum-field Rabi splitting). We have employed this splitting to generate squeezing with observed reductions in photocurrent noise of 30 % below the shot-noise level. A degree of squeezing of ~50% is inferred for the field state in the absence of propagation and detection losses. Squeezing has been observed in two different cavity geometries with quite different coupling coefficients. In each case, the frequency of best squeezing corresponds to that of the normal mode splitting g N (g= single atom coupling coefficent and N = number of atoms) in good agreement with our theoretical predictions. Regions of parameter space with very large degrees of squeezing (>20×) are identified. Preliminary extensions of the theory into a transient regime with (cavity lifetime) ≪ (interaction time) ≪ (atomic lifetime) are described.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Interaction of a two-level atom with a cavity mode in the bad-cavity limit

J. I. Cirac

The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.

Physical Review A•Oct 1, 1992•95 citations
We investigate the effect of a spatially varying field mode on the squeezing generated by two-level atoms interacting with a single mode of an optical cavity. The mode structure is incorporated into a quantum theory that does not employ adiabatic elimination of field or atomic variables. Thus we are able to consider the regime in which cavity and atomic decay rates are approximately equal as well as the good- and bad-cavity limits. Calculations show that squeezing is reduced by the inclusion of a Gaussian transverse mode profile and a standing-wave structure for a particular value of atomic cooperativity C. The model is consistent with recent measurements of squeezing. The degree of squeezing reduction depends on the ratio of cavity and atomic damping rates, in the regime where they are similar in size.
A spatially varying field mode is included in calculating the squeezing effect for a system of two-level atoms in the good-cavity limit. Two examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are used to demonstrate the quite general method. In qualitative terms, the squeezing predicted for plane waves is preserved. However, for a given value of atomic cooperativity parameter C, there is a degradation in squeezing because of the spatially varying field structure.
Squeezed state generation for a system of two-level atoms interacting with the field of a high-finesse cavity has been extensively discussed both experimentally and theoretically in recent years. Most theories describing these systems take the cavity field as a plane traveling wave for simplicity. With this assumption it is quite difficult to make quantitative comparisons between theory and recent experiments. However, by employing the formalism developed in Ref. 1, we are able to treat rather general spatial variations of the intracavity field subject to the constraint of the good-cavity limit of optical bistability. Squeezed state generation for the three particular examples of a plane-wave ring interferometer, a Gaussian-mode ring cavity, and a plane-wave field in a standing-wave interferometer are considered to illustrate the formalism. Somewhat surprisingly, in regimes for which the plane-wave theory predicts 50-70% squeezing (cooperatively C ~102–103), the standing-wave structure produces only modest reductions in the squeezing (a few percent), while the radial variations of the field reduce the squeezing by ~10%.
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 give a general theory of the interaction of a large number of two-level atoms in an optical cavity driven by a broadband squeezed input of finite amplitude. No adiabatic elimination of atoms or field is made, and atomic and cavity loss and dispersion are fully incorporated in the theory. We calculate the optical and squeezing spectra that may be observed in transmission and reflection from the cavity; the latter exhibits a novel interference structure superimposed as a result of the squeezed input. Results presented indicate that it is possible to somewhat reduce the vacuum Rabi peaks in transmission, in the strong-coupling regime, with a moderately squeezed input. In the limit of a ``bad cavity,'' the characteristic triplet transmitted under conditions of saturation may have one of its sidebands suppressed and the other enhanced by a squeezed input. These signatures suggest new alternatives for the experimental study of the interaction of atoms with squeezed light.
A theoretical and experimental investigation of the generation of squeezed states of light has been carried out for a system of two-level atoms inside a high-finesse cavity. The regime that we consider is such that the coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom-field system (the so-called vacuum-field Rabi splitting). We have employed this splitting to generate squeezing with observed reductions in photocurrent noise of 30 % below the shot-noise level. A degree of squeezing of ~50% is inferred for the field state in the absence of propagation and detection losses. Squeezing has been observed in two different cavity geometries with quite different coupling coefficients. In each case, the frequency of best squeezing corresponds to that of the normal mode splitting g N (g= single atom coupling coefficent and N = number of atoms) in good agreement with our theoretical predictions. Regions of parameter space with very large degrees of squeezing (>20×) are identified. Preliminary extensions of the theory into a transient regime with (cavity lifetime) ≪ (interaction time) ≪ (atomic lifetime) are described.
The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.