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

Quantum jumps between dressed states: A proposed cavity-QED test using feedback

Joseph E. Reiner, Howard M. Wiseman, Hideo Mabuchi

Published Apr 11, 2003• 15 citations
Publisher

Abstract

A strongly driven cavity containing a single resonant strongly coupled atom exhibits a phase bistability. The phase of the field is strongly correlated with the phase of the atomic dipole. It has been shown previously that phase-sensitive monitoring of the field emitted by the cavity would induce conditional quantum jumps between orthogonal atomic dipole states (``dressed'' states). Here we show that such monitoring can be used to fix the atom into a single dressed state. As soon as a state-changing quantum jump is inferred from the measurement of the field, the atomic state is flipped using a $\ensuremath{\pi}$ pulse. We study this feedback scheme analytically and numerically. We show that the occupation probability of the desired fixed state can be as high as $1\ensuremath{-}1/8\ensuremath{\eta}{C}_{1},$ where ${C}_{1}\ensuremath{\gg}1$ is the single-atom cooperativity and $\ensuremath{\eta}$ the detection efficiency (which does not have to be close to unity). The control of the atomic dynamics is manifest in the fluorescence spectrum. The widths of all three peaks are modified from the usual Mollow spectrum, and almost all of the area under one of the sidebands is transferred to the other sideband. This is as expected, as one of the dressed states is essentially unoccupied, and transitions out of it do not occur. In addition, the width of the central peak goes to zero. This indicates coherent scattering due to the nonzero mean atomic dipole created by the feedback.

DOI
10.1103/physreva.67.042106

Related papers

Quantum trajectory calculations in cavity QED

L. Tian, H. J. Carmichael

We use the quantum trajectory (stochastic wave function) approach to simulate the dynamics of a cavity QED system. The system consists of one atom interacting on resonance with one mode of a coherently driven optical cavity. We simulate a variety of different measurements on this system. The simulation of direct photoelectric detection produces trajectories that illustrate the collapse of the wave function in delayed photon coincidence measurements. It also allows us to calculate waiting-time distributions, pho­toelectron counting distributions, and the mean transmitted intensity as a function of the excitation frequency and field strength. A simulation with frequency filtering of the stochastic wave fuction gives results for optical spectra. From a simulation of homodyne detection we obtain trajectories showing the fluctuations in the quadrature phase amplitudes of the intracavity field and the atomic dipole. These simulations are used to calculate spectra of squeezing. We show that when the cavity is excited near one of the "vacuum" Rabi resonances, the composite atom-cavity system behaves like a two-state system. Under these conditions the optical spectrum shows Mollow sidebands caused by a dynamic Stark shift of the Jaynes-Cummings eigenstates. Thus, in this measurement we are observing the "dressing" of the (one-quantum) dressed states.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Quantum jumps in a two-level atom: Simple theories versus quantum trajectories

Howard M. Wiseman, Gilman E. S. Toombes

A strongly driven $(\ensuremath{\Omega}\ensuremath{\gg}\ensuremath{\gamma})$ two-level atom relaxes towards an equilibrium state $\ensuremath{\rho}$ which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $\ensuremath{\rho}$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed-atom theory is also supposed to describe the quantum jumps of an individual atom due to photoemissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $\ensuremath{\rho}$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection), and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed-state model, with errors of order $\frac{3}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2/3},$ $\frac{1}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2}$, and $\frac{3}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2}$, respectively. The significance of this result to the program of environmentally induced superselection is discussed.

Physical Review A•Sep 1, 1999•31 citations

Quantum jumps in a two-level atom

Howard M. Wiseman, Gilman E. S. Toombes

A strongly-driven ($Ω>> γ$) two level atom relaxes towards an equilibrium state rho which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $ρ$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed atom theory is also supposed to describe the quantum jumps of an individual atom due to photo-emissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $ρ$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are: spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection) and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed state model, with errors of order $(3/4) (γ/Ω)^{2/3}$, $(1/4) (γ/Ω)^{2}$, and $(3/4) (γ/Ω)^{2}$ respectively. The significance of this result to the program of environmentally-induced superselection is discussed.

arXiv:quant-ph/9903023•Mar 5, 1999•2 citations

Dynamics of a driven two-level atom coupled to a frequency-tunable cavity

Peng Zhou, S. Swain

A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.

Physical Review A•Aug 1, 1998•35 citations

Experiments in two-mode cavity QED

D. G. Norris

Cavity quantum electrodynamics (QED) allows the study of light-matter in-teractions at the most basic level, through precise identification of the coherent and incoherent (dissipative) parts of the system evolution. We present measurements of light from a cavity QED system consisting of a high-finesse optical resonator coupled to a beam of cold Rb atoms. The novelty of the design lies in the interplay of two degenerate and orthogonal polarization modes. One mode (driven) behaves as the canonical cavity mode of the Jaynes-Cummings Hamiltonian, coherently exciting the atoms with a modest coupling strength; the other mode (undriven) collects a small fraction of spontaneously emitted light and provides a probe of the dissipative processes. We first demonstrate the ability to detect individual atoms passing through the cavity modes in real time by coincidence detection of photons from the un-driven mode. Calculation of statistics and correlation functions from the complete photon detection record allows the determination of detection probabilities and the reconstruction of atomic trajectories. We next present evidence of quantum coher-ence that is created, modified, and measured in the excitation-spontaneous emission cycle. The coherence appears as a long-lived quantum beat at the ground-state Larmor frequency, visible in the intensity autocorrelation function of the undriven mode. Quantum jumps of the atomic state, occurring in between the detections of photons from the cavity, result in substantial changes in the frequency and spectral width of the beats. We present the results of a full quantum Monte Carlo calculation in order to quantitatively explain the measurements.

•Jan 1, 2011•0 citations

Cavity-induced modifications of quantum jumps

Joachim von Zanthier, G. S. Agarwal, HERBERT WALTHER

Complete density-matrix equations and a one-photon counting probability are used to examine the photon statistics of fluorescence light of a single three-level atom, weakly coupled to an external cavity of low $Q$ value. The internal structure of the atom is supposed to be characterized by a weak and a strong transition. The strong transition is coherently driven by an external laser field, whereas no external field is acting on the weak transition. In free space the system exhibits quantum jumps. By placing the atom within the mirrors of an external cavity, tuned close to the transition frequency of the two upper levels, modifications in the quantum jump behavior of the atom are shown due to a modified spontaneous decay rate between the two states. In particular, it is demonstrated that the effect of the cavity is to modify the repetition rate of quantum jumps into the metastable dark state and the average duration of bright periods of fluorescence, whereas the average duration of dark periods is not changed in first order of the spontaneous decay rates involved. In view of current experiments in our laboratory a quantitative analysis is presented for the special case of a single indium ion located between the mirrors of a high-order symmetric confocal cavity.

Physical Review A•Sep 1, 1997•1 citation
A strongly driven cavity containing a single resonant strongly coupled atom exhibits a phase bistability. The phase of the field is strongly correlated with the phase of the atomic dipole. It has been shown previously that phase-sensitive monitoring of the field emitted by the cavity would induce conditional quantum jumps between orthogonal atomic dipole states (``dressed'' states). Here we show that such monitoring can be used to fix the atom into a single dressed state. As soon as a state-changing quantum jump is inferred from the measurement of the field, the atomic state is flipped using a \ensuremathπ\ensuremath{\pi}\ensuremathπ pulse. We study this feedback scheme analytically and numerically. We show that the occupation probability of the desired fixed state can be as high as 1\ensuremath−1/8\ensuremathηC1,1\ensuremath{-}1/8\ensuremath{\eta}{C}_{1},1\ensuremath−1/8\ensuremathηC1​, where C1\ensuremath≫1{C}_{1}\ensuremath{\gg}1C1​\ensuremath≫1 is the single-atom cooperativity and \ensuremathη\ensuremath{\eta}\ensuremathη the detection efficiency (which does not have to be close to unity). The control of the atomic dynamics is manifest in the fluorescence spectrum. The widths of all three peaks are modified from the usual Mollow spectrum, and almost all of the area under one of the sidebands is transferred to the other sideband. This is as expected, as one of the dressed states is essentially unoccupied, and transitions out of it do not occur. In addition, the width of the central peak goes to zero. This indicates coherent scattering due to the nonzero mean atomic dipole created by the feedback.
We use the quantum trajectory (stochastic wave function) approach to simulate the dynamics of a cavity QED system. The system consists of one atom interacting on resonance with one mode of a coherently driven optical cavity. We simulate a variety of different measurements on this system. The simulation of direct photoelectric detection produces trajectories that illustrate the collapse of the wave function in delayed photon coincidence measurements. It also allows us to calculate waiting-time distributions, pho­toelectron counting distributions, and the mean transmitted intensity as a function of the excitation frequency and field strength. A simulation with frequency filtering of the stochastic wave fuction gives results for optical spectra. From a simulation of homodyne detection we obtain trajectories showing the fluctuations in the quadrature phase amplitudes of the intracavity field and the atomic dipole. These simulations are used to calculate spectra of squeezing. We show that when the cavity is excited near one of the "vacuum" Rabi resonances, the composite atom-cavity system behaves like a two-state system. Under these conditions the optical spectrum shows Mollow sidebands caused by a dynamic Stark shift of the Jaynes-Cummings eigenstates. Thus, in this measurement we are observing the "dressing" of the (one-quantum) dressed states.
A strongly driven $(\ensuremath{\Omega}\ensuremath{\gg}\ensuremath{\gamma})$ two-level atom relaxes towards an equilibrium state $\ensuremath{\rho}$ which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $\ensuremath{\rho}$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed-atom theory is also supposed to describe the quantum jumps of an individual atom due to photoemissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $\ensuremath{\rho}$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection), and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed-state model, with errors of order $\frac{3}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2/3},$ $\frac{1}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2}$, and $\frac{3}{4}(\ensuremath{\gamma}/\ensuremath{\Omega}{)}^{2}$, respectively. The significance of this result to the program of environmentally induced superselection is discussed.
A strongly-driven (Ω>>γΩ>> γΩ>>γ) two level atom relaxes towards an equilibrium state rho which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of ρρρ. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed atom theory is also supposed to describe the quantum jumps of an individual atom due to photo-emissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of ρρρ. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are: spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection) and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed state model, with errors of order (3/4)(γ/Ω)2/3(3/4) (γ/Ω)^{2/3}(3/4)(γ/Ω)2/3, (1/4)(γ/Ω)2(1/4) (γ/Ω)^{2}(1/4)(γ/Ω)2, and (3/4)(γ/Ω)2(3/4) (γ/Ω)^{2}(3/4)(γ/Ω)2 respectively. The significance of this result to the program of environmentally-induced superselection is discussed.
A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.
Cavity quantum electrodynamics (QED) allows the study of light-matter in-teractions at the most basic level, through precise identification of the coherent and incoherent (dissipative) parts of the system evolution. We present measurements of light from a cavity QED system consisting of a high-finesse optical resonator coupled to a beam of cold Rb atoms. The novelty of the design lies in the interplay of two degenerate and orthogonal polarization modes. One mode (driven) behaves as the canonical cavity mode of the Jaynes-Cummings Hamiltonian, coherently exciting the atoms with a modest coupling strength; the other mode (undriven) collects a small fraction of spontaneously emitted light and provides a probe of the dissipative processes. We first demonstrate the ability to detect individual atoms passing through the cavity modes in real time by coincidence detection of photons from the un-driven mode. Calculation of statistics and correlation functions from the complete photon detection record allows the determination of detection probabilities and the reconstruction of atomic trajectories. We next present evidence of quantum coher-ence that is created, modified, and measured in the excitation-spontaneous emission cycle. The coherence appears as a long-lived quantum beat at the ground-state Larmor frequency, visible in the intensity autocorrelation function of the undriven mode. Quantum jumps of the atomic state, occurring in between the detections of photons from the cavity, result in substantial changes in the frequency and spectral width of the beats. We present the results of a full quantum Monte Carlo calculation in order to quantitatively explain the measurements.
Complete density-matrix equations and a one-photon counting probability are used to examine the photon statistics of fluorescence light of a single three-level atom, weakly coupled to an external cavity of low QQQ value. The internal structure of the atom is supposed to be characterized by a weak and a strong transition. The strong transition is coherently driven by an external laser field, whereas no external field is acting on the weak transition. In free space the system exhibits quantum jumps. By placing the atom within the mirrors of an external cavity, tuned close to the transition frequency of the two upper levels, modifications in the quantum jump behavior of the atom are shown due to a modified spontaneous decay rate between the two states. In particular, it is demonstrated that the effect of the cavity is to modify the repetition rate of quantum jumps into the metastable dark state and the average duration of bright periods of fluorescence, whereas the average duration of dark periods is not changed in first order of the spontaneous decay rates involved. In view of current experiments in our laboratory a quantitative analysis is presented for the special case of a single indium ion located between the mirrors of a high-order symmetric confocal cavity.