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

Bloch-vector model for dressed states of resonant Raman interaction

M. S. Shahriar, Philip Hemmer

Published Jan 1, 1990• 0 citations
Publisher

Abstract

It is well known that the resonant Raman interaction optically pumps atoms into a non-absorbing dressed-state.1 When this state is long-lived compared to the optical Rabi frequencies and the decay rate of the intermediate state, many interesting dynamics arise. These dynamics are significant in applications such as Raman clock AC–Stark shifts, microwave phase-sensitive optical absorption,2 and Raman cooling. By using appropriate approximations, we show that these dynamics can be well described with a Bloch-vector model, which involves only ground-state populations and coherence. This ground-state Bloch-vector model resembles the Bloch-vector model of a two-level system, but it has subtly different dynamics. Furthermore, we construct a novel dressed-state Bloch-vector that clearly shows the analogy between conventional optical pumping and coherent Raman trapping. In this model, one dressed-state is a nonabsorbing state, and the other is an absorbing state. We use the dressed-state Bloch vector to show how Raman AC–Stark shift arises and how it depends on experimental parameters. We also show how the microwave phase-sensitive optical absorption can be quantitatively calculated in a simple way.

DOI
10.1364/oam.1990.thu2

Related papers

A simple model of laser without inversion

P. Ru, L. M. Narducci, Marlan O. Scully +1 more

The emergence of laser action from an atomic system without population inversion is beginning to attract theoretical and experimental attention as a possible way of generating useful coherent radiation at unusual wavelengths. The goal of this communication is to clarify the physical origin of this phenomenon using a four-level system whose ground state consists of two quasidegenerate levels that are coupled to a higher-lying state by a Raman-like transition. In the presence of the ground-state coherence induced by the Raman field, we calculate the absorption spectrum of a weak probe whose tunable frequency scans across the transition frequencies between the two ground-state levels and another higher-lying state that may or may not be weakly excited by an incoherent pump mechanism. Our calculation, based on a dressed atomic state approach, clarifies the conditions that must be satisfied to produce gain, identifies the frequency (or frequencies) at which the gain is maximum, and elucidates the functions of the incoherent pump, the Raman field, and the coherence between the ground-state levels in this process. An appropriate set of Maxwell- Bloch equations for a ring-cavity model of this system confirms the appearance of laser action when the small-signal gain conditions are satisfied.

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

Absorption with inversion and amplification without inversion in a coherently prepared V system: A dressed-state approach

Doron Braunstein, R. Shuker

Light-induced absorption with population inversion and amplification without population inversion in a coherently prepared closed three level V-type system are investigated. This study is performed from the point of view of a two color dressed-state basis. Both of these processes are possible due to atomic coherence and quantum interference contrary to simple intuitive predictions. Merely on a physical basis, one would expect a complementary process to the amplification without inversion. We believe that absorption in the presence of population inversion found in the dressed-state picture utilized in this study, constitutes such a process. We derive approximate analytic time-dependent solutions, for coherences and populations that are compared with full numerical solutions exhibiting good agreement. Steady-state quantities are also calculated, and the conditions under which the system exhibits absorption and gain with and without inversion, in the dressed-state representation are derived. It is found that for weak input probe-laser field absorption with inversion and amplification without inversion may occur, for a range of system parameters. These take place at resonance and the generalized Rabi ac Stark-shifted frequencies, in agreement with exprimental investigations, and at beat frequencies, depending on the relevant parameters.

arXiv:quant-ph/9807014•Physical Review A•Oct 12, 2001•31 citations

Dark-state-based three-element vector model for the stimulated Raman interaction

M. S. Shahriar, Philip Hemmer, D. P. Katz +2 more

In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a \ensuremath{\Lambda} system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.

Physical Review A•Mar 1, 1997•66 citations

Optical parametric resonances

P. Thomann

The response of a two-level atom driven by a strong resonant amplitude-modulated field is calculated in the Bloch model. The population difference and dipole moment show a resonant behaviour when the Rabi frequency is a multiple of the modulation frequency. This phenomenon is related to the resonant AC Stark effect and is the optical counterpart of the coherence resonances known in radiofrequency magnetic resonance.

Journal of Physics B Atomic and Molecular Physics•Oct 1, 1976•19 citations

Nonlinear optical response of three-level systems

Raanan Bavli, Donald F. Heller, Y. B. Band

We investigate the properties of a homogeneously broadened three-level system interacting with two optical fields, Eω1(x,t) and Eω2(x,t), with central frequencies ω1 and ω2 whose amplitudes are assumed to be slowly varying in time compared with dephasing times of the optical transitions. We calculate Raman susceptibilities allowing each transition to be induced by both fields and without employing the rotating wave approximation (RWA); this enables correct calculation of the optical response of the medium when the fields are on-resonance or arbitrarily far off-resonance with the Raman transition. In some frequency regions the RWA causes substantial errors. A distinction is drawn between two different types of RWA: (a) a neglect of off-resonant components of the polarization for direct optical transitions, and (b) neglect of off-resonant components of off-diagonal density matrix elements of order Eω1(x,t)Eω2(x,t)* in the field amplitudes. The first RWA is known to become inaccurate when the pump frequency is significantly off-resonance with the pump transition. We show that the second RWA becomes inaccurate when ‖ω1−ω2‖ is small or comparable to the active Raman mode frequency (even when the field are close to resonance). Calculations based upon our expressions show that when the pump frequency is close to resonance with the optical transition from the ground state, a nonlinear absorption at the Stokes shifted frequency occurs. This absorption can significantly decrease the Raman gain. Also, we find that Rabi splittings in a three-level system can occur even when the pulse durations of the incident fields are short compared with the T1 times of the system. We solve analytically for the optical response of the system to two fields of arbitrary strength and frequency. We analyze this solution and its perturbative expansion in the field amplitudes. We use the Maxwell–Bloch equations developed here to propagate time-dependent pulses.

The Journal of Chemical Physics•Dec 1, 1989•20 citations

Multiphoton Raman transitions and Rabi oscillations in driven spin systems

A. P. Saǐko, Siarhei A. Markevich, Ryhor Fedaruk

In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.

arXiv:1807.05086•Physical Review A•Oct 5, 2018•24 citations
It is well known that the resonant Raman interaction optically pumps atoms into a non-absorbing dressed-state.1 When this state is long-lived compared to the optical Rabi frequencies and the decay rate of the intermediate state, many interesting dynamics arise. These dynamics are significant in applications such as Raman clock AC–Stark shifts, microwave phase-sensitive optical absorption,2 and Raman cooling. By using appropriate approximations, we show that these dynamics can be well described with a Bloch-vector model, which involves only ground-state populations and coherence. This ground-state Bloch-vector model resembles the Bloch-vector model of a two-level system, but it has subtly different dynamics. Furthermore, we construct a novel dressed-state Bloch-vector that clearly shows the analogy between conventional optical pumping and coherent Raman trapping. In this model, one dressed-state is a nonabsorbing state, and the other is an absorbing state. We use the dressed-state Bloch vector to show how Raman AC–Stark shift arises and how it depends on experimental parameters. We also show how the microwave phase-sensitive optical absorption can be quantitatively calculated in a simple way.
The emergence of laser action from an atomic system without population inversion is beginning to attract theoretical and experimental attention as a possible way of generating useful coherent radiation at unusual wavelengths. The goal of this communication is to clarify the physical origin of this phenomenon using a four-level system whose ground state consists of two quasidegenerate levels that are coupled to a higher-lying state by a Raman-like transition. In the presence of the ground-state coherence induced by the Raman field, we calculate the absorption spectrum of a weak probe whose tunable frequency scans across the transition frequencies between the two ground-state levels and another higher-lying state that may or may not be weakly excited by an incoherent pump mechanism. Our calculation, based on a dressed atomic state approach, clarifies the conditions that must be satisfied to produce gain, identifies the frequency (or frequencies) at which the gain is maximum, and elucidates the functions of the incoherent pump, the Raman field, and the coherence between the ground-state levels in this process. An appropriate set of Maxwell- Bloch equations for a ring-cavity model of this system confirms the appearance of laser action when the small-signal gain conditions are satisfied.
Light-induced absorption with population inversion and amplification without population inversion in a coherently prepared closed three level V-type system are investigated. This study is performed from the point of view of a two color dressed-state basis. Both of these processes are possible due to atomic coherence and quantum interference contrary to simple intuitive predictions. Merely on a physical basis, one would expect a complementary process to the amplification without inversion. We believe that absorption in the presence of population inversion found in the dressed-state picture utilized in this study, constitutes such a process. We derive approximate analytic time-dependent solutions, for coherences and populations that are compared with full numerical solutions exhibiting good agreement. Steady-state quantities are also calculated, and the conditions under which the system exhibits absorption and gain with and without inversion, in the dressed-state representation are derived. It is found that for weak input probe-laser field absorption with inversion and amplification without inversion may occur, for a range of system parameters. These take place at resonance and the generalized Rabi ac Stark-shifted frequencies, in agreement with exprimental investigations, and at beat frequencies, depending on the relevant parameters.
In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a \ensuremath{\Lambda} system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.
We investigate the properties of a homogeneously broadened three-level system interacting with two optical fields, Eω1(x,t) and Eω2(x,t), with central frequencies ω1 and ω2 whose amplitudes are assumed to be slowly varying in time compared with dephasing times of the optical transitions. We calculate Raman susceptibilities allowing each transition to be induced by both fields and without employing the rotating wave approximation (RWA); this enables correct calculation of the optical response of the medium when the fields are on-resonance or arbitrarily far off-resonance with the Raman transition. In some frequency regions the RWA causes substantial errors. A distinction is drawn between two different types of RWA: (a) a neglect of off-resonant components of the polarization for direct optical transitions, and (b) neglect of off-resonant components of off-diagonal density matrix elements of order Eω1(x,t)Eω2(x,t)* in the field amplitudes. The first RWA is known to become inaccurate when the pump frequency is significantly off-resonance with the pump transition. We show that the second RWA becomes inaccurate when ‖ω1−ω2‖ is small or comparable to the active Raman mode frequency (even when the field are close to resonance). Calculations based upon our expressions show that when the pump frequency is close to resonance with the optical transition from the ground state, a nonlinear absorption at the Stokes shifted frequency occurs. This absorption can significantly decrease the Raman gain. Also, we find that Rabi splittings in a three-level system can occur even when the pulse durations of the incident fields are short compared with the T1 times of the system. We solve analytically for the optical response of the system to two fields of arbitrary strength and frequency. We analyze this solution and its perturbative expansion in the field amplitudes. We use the Maxwell–Bloch equations developed here to propagate time-dependent pulses.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.