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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Collective quantum dynamics of an atomic lattice coupled to an optical resonator

Stefano Zippilli, Giovanna Morigi, János K. Asbóth, Helmut Ritsch

Published Jan 25, 2006• 0 citations
Publisher

Abstract

We study the quantum dynamics of an array of coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. In this configuration atomic excitation is suppressed even for strong driving fields, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of this interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest when the atoms are ordered in a wavelength spaced lattice placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. We analyze the mechanical forces in the regime where the interference condition is fulfilled, and show that the atomic pattern is mechanically stable whenever the driving frequency is red detuned with respect to the cavity frequency, irrespective of the atomic transition frequency

DOI
10.1109/cleoe.2005.1568482

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We study the quantum dynamics of an array of coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. In this configuration atomic excitation is suppressed even for strong driving fields, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of this interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest when the atoms are ordered in a wavelength spaced lattice placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. We analyze the mechanical forces in the regime where the interference condition is fulfilled, and show that the atomic pattern is mechanically stable whenever the driving frequency is red detuned with respect to the cavity frequency, irrespective of the atomic transition frequency
We study thequantum dynamics ofanarray ofcoherently driven two-level atomscoupled toanoptical resonator. The setupt isdepicted inthefigure [1]. Inthestrong coupling regime thecavity field generated byatomic scattering interferes destructively withthepumpontheatoms. Inthis configuration atomic excitation issuppressed evenforstrong driving fields, while thestationary intracavity field amplitude isalmost independent oftheatomnumber. Themagnitude ofthis interference effect depends onthedetuning between laser andcavity field andontherelative atomic positions andis strongest whentheatoms areordered inawavelength spaced lattice placed attheantinodes ofthecavity mode. Inthis case three dimensional intensity minima arecreated inthevicinity ofeachatom[1]. Weanalyze themechanical forces inthe regime wheretheinterference condition isfulfilled, andshowthat theatomic pattern ismechanically stable whenever the driving frequency isreddetuned withrespect tothecavity frequency, irrespective oftheatomic transition frequency. Hence atomic self organization, aspredicted in[2]canalso occurintheparameter regime wheresuperradiant scattering is suppressed bycollective interference. Wediscuss howthese results giveanewkeytounderstand recent experiments oncollective cavity cooling andmayallow toimplement fast tailored atom-atom interactions aswellasnonperturbative particle detection withverysmall energy transfer. I -_~~
When N driven atoms emit in phase into a high-Q cavity mode, the intracavity field generated by collective scattering interferes destructively with the pump driving the atoms. Hence atomic fluorescence is suppressed and cavity loss becomes the dominant decay channel for the whole ensemble. Microscopically, 3D light-intensity minima are formed in the vicinity of the atoms that prevent atomic excitation and form a regular lattice. The effect gets more pronounced for large atom numbers, when the sum of the atomic decay rates exceeds the rate of cavity losses and one would expect the opposite behavior. These results provide new insight into recent experiments on collective atomic dynamics in cavities.
Abstract By considering linear scattering of laser-driven cold atoms inside an undriven high-finesse optical resonator, we experimentally demonstrate effects unique to a strongly coupled vacuum field. Arranging the atoms in an incommensurate lattice with respect to the radiation wavelength, the Bragg scattering into the cavity can be suppressed by destructive interference: the atomic array is subradiant to the cavity mode under transverse illumination. We show however, that strong collective coupling leads to a drastic modification of the excitation spectrum, as evidenced by well-resolved vacuum Rabi splitting in the intensity of the fluctuations. Furthermore, we demonstrate a significant polarization rotation in the linear scattering off the subradiant array via Raman scattering induced by the strongly coupled vacuum field.
We investigate the behaviour of the intracavity field in a strongly coupled atom–cavity system (a collection of two-level atoms inside a high-Q cavity) driven by a short strong external resonant pulse. A new effect is predicted, the amplification of the intracavity field appears if the atomic number density in a cavity exceeds the instability threshold which is proportional to the square of the strong driving field. The amplification gain is proportional to the amplitude of the strong driving field. The amplitude of the intracavity field in the vicinity of a critical point above the threshold is time-dependent modulated with harmonics of half of the Rabi frequency of the driving field.
We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.
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.