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 Physics B Atomic Molecular and Optical Physics

Coherent population trapping via quantum interference of incoherent pump processes in three-level systems

Xiangming Hu, Jie-Peng Zhang

Published Dec 17, 2003• 19 citations
Publisher

Abstract

Quantum interference has been predicted to occur in a three-level Λ system with near-degenerate dipole allowed transitions, which are coupled to the same linearly polarized incoherent field. For the Λ system with two degenerate lower levels, we show that (a) quantum interference of incoherent pump processes leads to coherent population trapping (CPT), and (b) when two coherent fields are applied to two transitions on two-photon resonance, CPT appears when the amplitudes and phases of the applied coherent fields and the polarization angle of the incoherent field satisfy certain conditions. Further, the physical mechanism and the above conditions for CPT are presented.

DOI
10.1088/0953-4075/37/2/004

Related papers

Inducing quantum coherence via decays and incoherent pumping with application to population trapping, lasing without inversion, and quenching of spontaneous emission

Victor V. Kozlov, Yuri V. Rostovtsev, Marlan O. Scully

Quantum interference in a decaying three-level system of V type with degenerate upper levels driven by a single incoherent field is shown to lead to a coherent population-trapping state and more generally to a population-locked state. The latter is a state with half the population locked in two upper states regardless of the strength of incoherent pumping and decay rates. We reveal the mechanism by which half the population is pumped to the upper states no matter how weak is the incoherent pumping. Transient regimes of gain without inversion and inversion without gain are demonstrated. Quenching of spontaneous emission due to electron collisions is also discussed in support of the experiments and ideas of Suckewer and [Phys. Rev. Lett. 60, 1122 (1988)].

Physical Review A•Dec 26, 2006•85 citations

Phase-dependent atomic coherence and interference in multi-level atomic systems

Jiepeng Zhang, Yifu Zhu

Atomic coherence and interference manifested by electromagentically induced transparency (EIT) and coherent population trapping (CPT) plays an important role in the current studies of atom-photon interactions and has found numerous applications in optical physics. EIT is created in a three-level atomic system by a coupling field and results in destructive interference between two excitation paths of a weak probe laser interacting with the atomic medium. This leads to suppressed linear absorption and rapidly varying atomic dispersion for the probe laser near the atomic resonance, which provides the platform for a variety of applications such as nonlinear optics at low light levels, slow light manipulation, and quantum state engineering for photons and atoms. Here we extend the simple three-level EIT system to more complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced: either constructive or destructive interference can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT configuration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system.

BENTHAM SCIENCE PUBLISHERS eBooks•Jan 1, 2009•0 citations

Interference effects in a three-level atom in a cavity beyond the weak-field approximation

David A. Cardimona, Paul M. Alsing, Henry Mozer +1 more

We investigate quantum interference and classical-interference effects when three-level atoms in the ``$\ensuremath{\Lambda}$'' or ``V'' configuration interact with both a cavity-field mode and an external driving field mode. We describe electromagnetically induced transparency ($\ensuremath{\Lambda}$ configuration), as well as a ``field-induced transparency'' (V configuration), and we go beyond the weak cavity-field studies of previous papers by utilizing a Heisenberg-picture density matrix approach. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with, the external pump field when the pump-field frequency equals the cavity frequency, a surprising effect found in two-level atoms in a cavity excited by an external pump field that persists in three-level atoms. The better the cavity, the quicker this buildup occurs. When the cavity field reaches this ``out-of-phase'' condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical-interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances when the state populations are coherently driven into a linear combination that is decoupled from any applied field and population is trapped in the excited states (``coherent population trapping''). When the cavity frequency is tuned to the frequency at which quantum interference would occur, the two interference effects compete with each other. The cavity field begins to evolve toward the $180\ifmmode^\circ\else\textdegree\fi{}$ out-of-phase condition, thereby approaching a classical destructive interference condition with the pump field. Then at some point before 100% classical interference occurs, depending on the cavity damping rate and atom/cavity coupling strength, the atom builds up its coherence between state populations to produce the quantum interference effect. At that point, the atom becomes transparent and resonance fluorescence disappears, including fluorescence into the cavity, thereby causing the cavity field to die away.

Physical Review A•Jun 11, 2009•17 citations

Effects of spontaneously generated coherence on the pump-probe response of a Λ system

Sunish Menon, G. S. Agarwal

Near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.

Physical Review A•May 1, 1998•219 citations

Phase conjugation and degenerate four-wave mixing in three-level systems

Govind Prasad Agrawal

Considers phase conjugation through degenerate four-wave mixing in a Λ-type three-level system under certain simplifying assumptions, the most restrictive among them being the assumption of symmetrical detuning of the pump from the two lower lying sublevels. When compared to an absorbing resonant two-level system, it is found that significantly higher values of the phase-conjugate reflectivity are possible at pump intensities well below saturation provided the sublevel splitting is less than a homogeneous linewidth. The physical mechanism responsible for phase conjugation is coherent population trapping arising from two-photon-induced atomic coherence between the two sublevels.

IEEE Journal of Quantum Electronics•Dec 1, 1981•18 citations

Direct Observation of Coherent Population Trapping in a Superconducting Artificial Atom

William R. Kelly, Zachary Dutton, J. Schlafer +4 more

The phenomenon of coherent population trapping (CPT) of an atom (or solid state "artificial atom"), and the associated effect of electromagnetically induced transparency (EIT), are clear demonstrations of quantum interference due to coherence in multilevel quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a Lambda-type configuration, utilizing the three lowest lying levels of a local minimum of a phase qubit. We observe 60(+/-7)% suppression of the excited state population under conditions of CPT resonance. We present data and matching theoretical simulations showing the development of CPT in time. Finally, we used the observed time dependence of the excited state population to characterize quantum dephasing times of the system.

arXiv:0912.3291•Physical Review Letters•Apr 20, 2010•115 citations
Quantum interference has been predicted to occur in a three-level Λ system with near-degenerate dipole allowed transitions, which are coupled to the same linearly polarized incoherent field. For the Λ system with two degenerate lower levels, we show that (a) quantum interference of incoherent pump processes leads to coherent population trapping (CPT), and (b) when two coherent fields are applied to two transitions on two-photon resonance, CPT appears when the amplitudes and phases of the applied coherent fields and the polarization angle of the incoherent field satisfy certain conditions. Further, the physical mechanism and the above conditions for CPT are presented.
Quantum interference in a decaying three-level system of V type with degenerate upper levels driven by a single incoherent field is shown to lead to a coherent population-trapping state and more generally to a population-locked state. The latter is a state with half the population locked in two upper states regardless of the strength of incoherent pumping and decay rates. We reveal the mechanism by which half the population is pumped to the upper states no matter how weak is the incoherent pumping. Transient regimes of gain without inversion and inversion without gain are demonstrated. Quenching of spontaneous emission due to electron collisions is also discussed in support of the experiments and ideas of Suckewer and [Phys. Rev. Lett. 60, 1122 (1988)].
Atomic coherence and interference manifested by electromagentically induced transparency (EIT) and coherent population trapping (CPT) plays an important role in the current studies of atom-photon interactions and has found numerous applications in optical physics. EIT is created in a three-level atomic system by a coupling field and results in destructive interference between two excitation paths of a weak probe laser interacting with the atomic medium. This leads to suppressed linear absorption and rapidly varying atomic dispersion for the probe laser near the atomic resonance, which provides the platform for a variety of applications such as nonlinear optics at low light levels, slow light manipulation, and quantum state engineering for photons and atoms. Here we extend the simple three-level EIT system to more complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced: either constructive or destructive interference can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT configuration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system.
We investigate quantum interference and classical-interference effects when three-level atoms in the ``$\ensuremath{\Lambda}$'' or ``V'' configuration interact with both a cavity-field mode and an external driving field mode. We describe electromagnetically induced transparency ($\ensuremath{\Lambda}$ configuration), as well as a ``field-induced transparency'' (V configuration), and we go beyond the weak cavity-field studies of previous papers by utilizing a Heisenberg-picture density matrix approach. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with, the external pump field when the pump-field frequency equals the cavity frequency, a surprising effect found in two-level atoms in a cavity excited by an external pump field that persists in three-level atoms. The better the cavity, the quicker this buildup occurs. When the cavity field reaches this ``out-of-phase'' condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical-interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances when the state populations are coherently driven into a linear combination that is decoupled from any applied field and population is trapped in the excited states (``coherent population trapping''). When the cavity frequency is tuned to the frequency at which quantum interference would occur, the two interference effects compete with each other. The cavity field begins to evolve toward the $180\ifmmode^\circ\else\textdegree\fi{}$ out-of-phase condition, thereby approaching a classical destructive interference condition with the pump field. Then at some point before 100% classical interference occurs, depending on the cavity damping rate and atom/cavity coupling strength, the atom builds up its coherence between state populations to produce the quantum interference effect. At that point, the atom becomes transparent and resonance fluorescence disappears, including fluorescence into the cavity, thereby causing the cavity field to die away.
Near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.
Considers phase conjugation through degenerate four-wave mixing in a Λ-type three-level system under certain simplifying assumptions, the most restrictive among them being the assumption of symmetrical detuning of the pump from the two lower lying sublevels. When compared to an absorbing resonant two-level system, it is found that significantly higher values of the phase-conjugate reflectivity are possible at pump intensities well below saturation provided the sublevel splitting is less than a homogeneous linewidth. The physical mechanism responsible for phase conjugation is coherent population trapping arising from two-photon-induced atomic coherence between the two sublevels.
The phenomenon of coherent population trapping (CPT) of an atom (or solid state "artificial atom"), and the associated effect of electromagnetically induced transparency (EIT), are clear demonstrations of quantum interference due to coherence in multilevel quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a Lambda-type configuration, utilizing the three lowest lying levels of a local minimum of a phase qubit. We observe 60(+/-7)% suppression of the excited state population under conditions of CPT resonance. We present data and matching theoretical simulations showing the development of CPT in time. Finally, we used the observed time dependence of the excited state population to characterize quantum dephasing times of the system.