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arXiv:1108.1931 · Physical Review A

Microcavities coupled to multilevel atoms

Sandra Isabelle Schmid, Jörg Evers

Published Nov 11, 2011• 9 citations
arXivHTMLPDF

Abstract

A three-level atom in the $\ensuremath{\Lambda}$ configuration coupled to a microcavity is studied. The two transitions of the atom are assumed to couple to different counterpropagating mode pairs in the cavity. We analyze the dynamics both in the strong-coupling and the bad-cavity limits. We find that, compared to a two-level setup, the third atomic state and the additional control field modes crucially modify the system dynamics and enable more advanced control schemes. All results are explained using appropriate dressed-state and eigenmode representations. As potential applications, we discuss optical switching and turnstile operations and detection of particles close to the resonator surface.

DOI
10.1103/physreva.84.053822

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A three-level atom in the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration coupled to a microcavity is studied. The two transitions of the atom are assumed to couple to different counterpropagating mode pairs in the cavity. We analyze the dynamics both in the strong-coupling and the bad-cavity limits. We find that, compared to a two-level setup, the third atomic state and the additional control field modes crucially modify the system dynamics and enable more advanced control schemes. All results are explained using appropriate dressed-state and eigenmode representations. As potential applications, we discuss optical switching and turnstile operations and detection of particles close to the resonator surface.
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.
A cavity-modified master equation is derived for a coherently driven, V-type three-level atom coupled to a single-mode cavity in the bad-cavity limit. We show that population inversion in both the bare- and dressed-state bases may be achieved, originating from the enhancement of the atom-cavity interaction when the cavity is resonant with an atomic dressed-state transition. The atomic populations in the dressed-state representation are analyzed in terms of the cavity-modified transition rates. The atomic fluorescence spectrum and probe absorption spectrum are also investigated, and it is found that the spectral profiles may be controlled by adjusting the cavity frequency. Peak suppression and line narrowing occur under the appropriate conditions.
We study the dynamics of a coupled cavity system composed of three cavities, and propose a scheme for the coherent manipulation of two collective atomic modes by a control atom. In the scheme, the control atom and two atomic ensembles interact with the local cavity mode, while the control atom is externally driven by a laser field. We show that under certain conditions, the dynamics of the whole system are reduced to an effective coherent coupling between the control atom and two collective atomic modes, while the cavity fields are only virtually excited. We also study the dynamics of the entanglement generation of the two distant collective atomic modes. The scheme provides a potential application for quantum-state engineering and quantum control.
We study the classically driven two-level system with its center-of-mass motion vibrating in a harmonic trap and coupled to the photons in a two-mode cavity. The first mode is resonant to the driving field and an electronic transition. The second mode is off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we investigate the quantum dynamics of the light emitted by the atom and the cavity modes. We analyze and compare the corresponding atomic and intracavity photon spectra for a range of the driving laser field and the cavity coupling strengths. The results provide better understanding of the effects of the laser field and atom-cavity coupling strengths on quantum interference effects and photon blockade, particularly the Mollow's triplet and the Autler-Townes splitting in the good and bad cavity limits.
We calculate the probe spectrum for multilevel atoms in a damped, weakly driven cavity supporting two degenerate orthogonally polarized modes. One mode is weakly driven by a linearly polarized external field. The atoms, initially prepared in a mF=0{m}_{F}=0mF​=0 hyperfine ground state, couple to the driven mode by making a $\ensuremath{\Delta}{m}_{F}=0$ transition and to the orthogonally polarized mode by making $\ensuremath{\Delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ transitions to other hyperfine sublevels. We compare probe spectra, the intensity of the driven mode, the undriven mode, and the atomic excitation probability as a function of the detuning of the driving laser from the cavity resonance for three- and four-level atomic models. In both cases the spectrum of the driven mode is a vacuum Rabi doublet familiar from the driven, damped Jaynes-Cummings model. The undriven mode spectrum is a triplet with the maximum on resonance for the three-level model while the four-level model has a four-peaked spectrum. We discuss the role of strong coupling to the undriven mode in accounting for the qualitative difference between the models.
We propose a realization of the quantum switch for coherent light fields for the fiber-coupled microdisk cavities. We demonstrate by combining numerical and analytical methods that both in strong coupling and bad cavity limits it is possible to change a system's behavior from being fully transparent to being fully reflective by varying the amplitude of the external control field. We remark that tuning the amplitude of the control field instead of cavity-atom coupling strength, which was suggested by S. Parkins et al., [Phys. Rev. A 90, 053822 (2014)] for two-level atoms and works only in the strong coupling limit, brings more control and tunability over the transmitted and reflected intensities. We also demonstrate the possibility of controlling the statistics of the input coherent field with the control field which opens the venue for obtaining quantum states of light.