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

Annual Meeting Optical Society of America

Propagation of quantum fluctuations through passive optical systems

Xiao Min, H. J. Kimble

Published Jan 1, 1986• 1 citation
Publisher

Abstract

By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.

DOI
10.1364/oam.1986.tuj4

Related papers

Squeezing and quantum effects in optics

M. D. Reid

In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.

•Jan 1, 1984•0 citations

Enhancement of photon antibunching by passive interferometry

Yujiang Qu, Min Xiao, G. S. Holliday +2 more

Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons ${\mathit{n}}_{0}$ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by ${\mathit{g}}^{(2)}$(0)-1\ensuremath{\approxeq}-1/${\mathit{n}}_{0}$ for large values of ${\mathit{n}}_{0}$. We show that when higher-order terms that are usually ignored in linearized treatments are retained, ${\mathit{g}}^{(2)}$(0) satisfies the lower bound ${\mathit{g}}^{(2)}$(0)\ensuremath{\ge}0 even for small values of ${\mathit{n}}_{0}$. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.

Physical Review A•Apr 1, 1992•10 citations

Squeezed states of light

Harry J. Kimble

Squeezed states of the electromagnetic field are characterized by a reduction of fluctuations for one of two quadrature phase amplitudes below the level of fluctuations for the vacuum state. This reduction is a manifestly quantum or nonclassical feature which is of great interest in its own right but also potentially important for precision measurement with sensitivity beyond the shot-noise or vacuum-state limit. We describe three different experiments in which squeezed light has been generated in our laboratory involving parametric downconversion, intracavity frequency doubling, and optical bistability with two-state atoms. By employing the squeezed light produced by a subthreshold optical parametric oscillator, we have achieved improvements in sensitivity beyond the vacuum-state limit for the detection of both phase and amplitude changes of the electromagnetic field. An alternate route to sensitivity beyond the vacuum-state limit is through quantum nondemolition measurement, where we have suggested and are implementing a scheme involving parametric conversion and polarization mixing.

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

INVESTIGATION OF QUANTUM FLUCTUATIONS IN A NONLINEAR INTERFEROMETER WITH HARMONIC GENERATION AND COHERENT INTERACTION OF LIGHT AND CS ATOMS

Prashant Srinivasan

In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.

•Aug 23, 2013•0 citations

Single-atom cavity-enhanced absorption with injected squeezed vacuum: photon statistics

Perry R. Rice, L. M. Pedrotti, J. Walden

We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Fluctuation theory in quantum-optical systems

L. A. Lugiato, Federico Casagrande, L. Pizzuto

We show that the most complete and accurate description of fluctuations in quantum-optical systems is that obtained using the generalized Wigner distribution for the macroscopic observables of the system. The smallness of the inverse of the saturation photon number entitles us to neglect the terms with derivatives of order higher than second order in the time-evolution equation for the quasiprobability distribution. This treatment allows us to also describe correctly nonclassical effects such as photon antibunching or "squeezing," which are maltreated or even destroyed if one neglects the atom-atom correlations. We derive and analyze the Fokker-Planck equation for the Wigner function in the case of the usual laser and compare the results with those following from other approaches. In the region very high above threshold we find a small antibunching effect, which was not discovered in previous treatments due to the neglect of atom-atom correlations.

Physical Review A•Dec 1, 1982•57 citations
By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.
In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.
Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons n0{\mathit{n}}_{0}n0​ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by g(2){\mathit{g}}^{(2)}g(2)(0)-1\ensuremath{\approxeq}-1/n0{\mathit{n}}_{0}n0​ for large values of n0{\mathit{n}}_{0}n0​. We show that when higher-order terms that are usually ignored in linearized treatments are retained, g(2){\mathit{g}}^{(2)}g(2)(0) satisfies the lower bound g(2){\mathit{g}}^{(2)}g(2)(0)\ensuremath{\ge}0 even for small values of n0{\mathit{n}}_{0}n0​. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.
Squeezed states of the electromagnetic field are characterized by a reduction of fluctuations for one of two quadrature phase amplitudes below the level of fluctuations for the vacuum state. This reduction is a manifestly quantum or nonclassical feature which is of great interest in its own right but also potentially important for precision measurement with sensitivity beyond the shot-noise or vacuum-state limit. We describe three different experiments in which squeezed light has been generated in our laboratory involving parametric downconversion, intracavity frequency doubling, and optical bistability with two-state atoms. By employing the squeezed light produced by a subthreshold optical parametric oscillator, we have achieved improvements in sensitivity beyond the vacuum-state limit for the detection of both phase and amplitude changes of the electromagnetic field. An alternate route to sensitivity beyond the vacuum-state limit is through quantum nondemolition measurement, where we have suggested and are implementing a scheme involving parametric conversion and polarization mixing.
In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
We show that the most complete and accurate description of fluctuations in quantum-optical systems is that obtained using the generalized Wigner distribution for the macroscopic observables of the system. The smallness of the inverse of the saturation photon number entitles us to neglect the terms with derivatives of order higher than second order in the time-evolution equation for the quasiprobability distribution. This treatment allows us to also describe correctly nonclassical effects such as photon antibunching or "squeezing," which are maltreated or even destroyed if one neglects the atom-atom correlations. We derive and analyze the Fokker-Planck equation for the Wigner function in the case of the usual laser and compare the results with those following from other approaches. In the region very high above threshold we find a small antibunching effect, which was not discovered in previous treatments due to the neglect of atom-atom correlations.