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 Modern Optics

Optical Bloch Equations in the Presence of Stochastic Broad-band Vacuum

Elke Kahler, Krzysztof Wódkiewicz

Published Mar 1, 1994• 2 citations
Publisher

Abstract

The atomic Bloch equations driven by a quantum noise are investigated in the framework of c-number multiplicative stochastic Rabi amplitudes. It is shown that the stochastic broad-band vacuum fluctuations can be incorporated in such a way that spontaneous absorption is removed. It is shown that the multiplicative stochastic noise with no spontaneous absorption is equivalent to the quantum vacuum noise. A stochastic model of the broad-band squeezed vacuum is introduced and investigated. From such a stochastic description the fast and the slow damping rates of the Bloch polarizations are obtained. The strong-field resonance fluorescence spectrum and the steady-state atomic inversion for the stochastic model of squeezed vacuum fluctuations are derived.

DOI
10.1080/09500349414550481

Related papers

Systems driven by colored squeezed noise: The atomic absorption spectrum

Helmut Ritsch, P. Zoller

We derive stochastic density-matrix equations for an atom strongly driven by finite-bandwidth squeezed light. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for c-number electric field amplitudes. Saturation properties and the weak-field absorption spectrum of a two-level atom embedded in finite-bandwidth squeezed light and driven by a coherent field are calculated. We discuss the effect of finite bandwidth of the squeezed light in obtaining subnatural linewidth in the atomic absorption spectra, based on nonperturbative solutions of the stochastic optical Bloch equations.

Physical Review A•Nov 1, 1988•90 citations

Atomic Transitions in Finite-Bandwidth Squeezed Light

Helmut Ritsch, P. Zoller

A stochastic density-matrix equation for an atom strongly driven by finite-bandwidth squeezed light is derived. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for $c$-number electric field amplitudes. The possibility of obtaining reduced atomic linewidths in the absorption spectrum of the atom embedded in colored squeezed light is discussed, based on nonperturbative solutions of stochastic optical Bloch equations.

Physical Review Letters•Aug 29, 1988•62 citations

Field-dependent atomic relaxation in a squeezed vacuum

Saad S. M. Hassan, T. Jarad, Ravinder Rupchand Puri +1 more

The relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.

Journal of Optics B Quantum and Semiclassical Optics•Sep 30, 2005•7 citations

Stochastic description of vacuum fluctuations

K. Wódkiewicz

It is shown that vacuum fluctuations can be incorporated in the atomic equations of motion as an external multiplicative stochastic process. From the quantum-electrodynamics (QED) vacuum-vacuum transition amplitude it is shown that under the standard Wigner-Weisskopf approximation, this external noise is a Gaussian white noise with an operator-valued diffusion. This property reflects the fundamental difference between QED and a purely stochastic theory in which atomic fluctuations are neglected. It is shown that spontaneous emission results from a stochastic average over this external noise. The role of vacuum and atomic fluctuations in such a process is exhibited.

Physical Review A•Sep 1, 1988•5 citations

Resonance fluorescence of a two-level atom in an off-resonance squeezed vacuum

Z. Ficek, Barry C. Sanders

The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 28, 1994•21 citations

Asymmetric probe-absorption spectrum and amplification without population inversion in a squeezed vacuum

Z. Ficek, William Smyth, S. Swain

A comprehensive study is made of the absorption spectrum of a weak-probe beam irradiating a two-level atom damped by a broadband squeezed vacuum and driven by a strong laser field. We show that for a resonant driving field whose phase does not coincide with the principal directions of the squeezing ellipse, the absorption spectrum is asymmetric and exhibits absorption-emission profiles at the Rabi sidebands. We find that this feature arises from unequal populations of the dressed states of the system, which occur when all components of the Bloch vector are coupled to the driving field. A symmetric spectrum with dispersionlike profiles at the Rabi sidebands is revealed for an off-resonant driving field. Furthermore, the spectrum may exhibit an emission profile at the central frequency, signifying an amplification of the probe beam. We point out that the amplification at the central component is not attributed to population inversion in both the atomic bare states and in the dressed atomic states. We find that the amplification originates from the coherent population oscillations and is impossible in the absence of the squeezed vacuum. In addition, we examine how these features are affected by the detuning of the driving field and an imperfect squeezed vacuum.

Physical Review A•Nov 1, 1995•31 citations
The atomic Bloch equations driven by a quantum noise are investigated in the framework of c-number multiplicative stochastic Rabi amplitudes. It is shown that the stochastic broad-band vacuum fluctuations can be incorporated in such a way that spontaneous absorption is removed. It is shown that the multiplicative stochastic noise with no spontaneous absorption is equivalent to the quantum vacuum noise. A stochastic model of the broad-band squeezed vacuum is introduced and investigated. From such a stochastic description the fast and the slow damping rates of the Bloch polarizations are obtained. The strong-field resonance fluorescence spectrum and the steady-state atomic inversion for the stochastic model of squeezed vacuum fluctuations are derived.
We derive stochastic density-matrix equations for an atom strongly driven by finite-bandwidth squeezed light. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for c-number electric field amplitudes. Saturation properties and the weak-field absorption spectrum of a two-level atom embedded in finite-bandwidth squeezed light and driven by a coherent field are calculated. We discuss the effect of finite bandwidth of the squeezed light in obtaining subnatural linewidth in the atomic absorption spectra, based on nonperturbative solutions of the stochastic optical Bloch equations.
A stochastic density-matrix equation for an atom strongly driven by finite-bandwidth squeezed light is derived. The quantum properties of the light are accounted for by a doubling of dimensions of the stochastic process for ccc-number electric field amplitudes. The possibility of obtaining reduced atomic linewidths in the absorption spectrum of the atom embedded in colored squeezed light is discussed, based on nonperturbative solutions of stochastic optical Bloch equations.
The relaxation process of a single two-level atom driven by an intense resonant coherent field is studied in the presence of a broadband squeezed vacuum field. Generalized forms for the self-field operator and the field-dependent damping coefficients are derived. In the steady state, positive atomic inversion (~5%) is shown for some range of the phase of the squeezed vacuum field. The squeezing-induced enhanced and asymmetric coherence (i.e.?non-zero dispersive atomic polarization) induces profound asymmetry in the side-bands of the Mollow fluorescent spectrum and the absorptive?dispersive spectra near the Rabi side-band frequencies. The case of two and three cooperative atoms, instead of a single atom, shows (i)?positive atomic inversion in the steady state for larger interval of the squeeze phase parameter and more enhanced extrema for the atomic polarization components and (ii) the extra side peaks in the fluorescent spectrum become asymmetric and of dispersive-like profile. Dressed-state analysis in the single-atom case with the field-dependent decay process in the presence of the squeezed vacuum field is presented and shows that the inequality of the (field-dependent) decay rates of the dressed states leads to more positive inversion in the dressed states as compared with the normal vacuum case.
It is shown that vacuum fluctuations can be incorporated in the atomic equations of motion as an external multiplicative stochastic process. From the quantum-electrodynamics (QED) vacuum-vacuum transition amplitude it is shown that under the standard Wigner-Weisskopf approximation, this external noise is a Gaussian white noise with an operator-valued diffusion. This property reflects the fundamental difference between QED and a purely stochastic theory in which atomic fluctuations are neglected. It is shown that spontaneous emission results from a stochastic average over this external noise. The role of vacuum and atomic fluctuations in such a process is exhibited.
The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.
A comprehensive study is made of the absorption spectrum of a weak-probe beam irradiating a two-level atom damped by a broadband squeezed vacuum and driven by a strong laser field. We show that for a resonant driving field whose phase does not coincide with the principal directions of the squeezing ellipse, the absorption spectrum is asymmetric and exhibits absorption-emission profiles at the Rabi sidebands. We find that this feature arises from unequal populations of the dressed states of the system, which occur when all components of the Bloch vector are coupled to the driving field. A symmetric spectrum with dispersionlike profiles at the Rabi sidebands is revealed for an off-resonant driving field. Furthermore, the spectrum may exhibit an emission profile at the central frequency, signifying an amplification of the probe beam. We point out that the amplification at the central component is not attributed to population inversion in both the atomic bare states and in the dressed atomic states. We find that the amplification originates from the coherent population oscillations and is impossible in the absence of the squeezed vacuum. In addition, we examine how these features are affected by the detuning of the driving field and an imperfect squeezed vacuum.