Normal-mode splitting with large collective cooperativity

Tuchman, A. K.; Long, Romain; Vrijsen, Geert; Boudet, J.; Lee, Jongmin; Kasevich, Mark A.

doi:10.1103/physreva.74.053821

Cited by 53 publications

(41 citation statements)

References 28 publications

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“…Instead of reducing the cavity-mode volume to achieve large g, the number of emitters N interacting with the field can be increased, leading to the collective strong-coupling regime, where the coupling rate scales as V N g [11,12]. Various experimental observations of cavity-mode spectra proportional to \/~Ng due to the collective coherent coupling with two [13,14] or multiple [15,16] emitters have been made, including the case of a multimode cavity [17], In solid-state systems, the coherent coupling between a cavity mode and an ensemble of emitters has been achieved in the classical regime with semiconductor quantum wells [7,18]. However, in the quantum regime the significant inhomogeneous broadening of emission from self-assembled quantum dots (QDs) has so far hindered the observation of collective coherent coupling for semiconductor-based quantum emitters.…”

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confidence: 97%

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Unconventional collective normal-mode coupling in quantum-dot-based bimodal microlasers

et al. 2015

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We analyze the occurrence of normal-mode coupling (NMC) in bimodal lasers attributed to the collective interaction of the cavity field with a mesoscopic number of quantum dots (QDs). In contrast to the conventional NMC, here we observe locking of the frequencies and splitting of the linewidths of the system's eigenmodes in the coherent coupling regime. The theoretical analysis of the incoherent regime is supported by experimental observations where the emission spectrum of one of the orthogonally polarized modes of a bimodal QD micropillar laser demonstrates a distinct two-peak structure.Introduction. The study of cavity quantum electrodynamics (CQED) in the strong-coupling regime between atomlike emitters and the confined light field of microcavities has been a subject of considerable attention. In the traditional CQED, low-mode volume resonators are used to enhance the coupling rate g between a single emitter and the field in comparison to the system damping rates. Prominent realizations of the strong coupling include experimental demonstrations of reversible exchange of excitation between a single emitter and the field from both atomic [1-3] and solid-state [4,5] systems. Typical evidence of the strong-coupling regime represents splitting of the two degenerate modes, i.e., normal-mode splitting, which is a consequence of normal-mode coupling (NMC), e.g., between the emitter polarization mode and the field mode leading to a doublet cavity transmission spectrum [6[. In addition, NMC occurs in exciton-photon and phonon-photon interactions [7] and optomechanical phenomena [8], where the cavity field couples to a mechanical mode [9[. In view of the variety of implications of the regime of coherent coupling (see, e.g., [10]), a different approach to achieve strong coupling has also attracted much attention. Instead of reducing the cavity-mode volume to achieve large g, the number of emitters N interacting with the field can be increased, leading to the collective strong-coupling regime, where the coupling rate scales as V N g [11,12]. Various experimental observations of cavity-mode spectra proportional to \/~Ng due to the collective coherent coupling with two [13,14] or multiple [15,16] emitters have been made, including the case of a multimode cavity [17], In solid-state systems, the coherent coupling between a cavity mode and an ensemble of emitters has been achieved in the classical regime with semiconductor quantum wells [7,18]. However, in the quantum regime the significant inhomogeneous broadening of emission from self-assembled quantum dots (QDs) has so far hindered the observation of collective coherent coupling for semiconductor-based quantum emitters.

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confidence: 97%

“…Ynikayel In many different situations (see, e.g.. Refs. [1][2][3][4][5][6][7][7][8][9][10][11][12][13][14][15][16][17][18]), by convention coherent coupling of two (nearly degenerate) modes is commonly explained by studying the eigenvalues of the system,…”

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confidence: 99%

Unconventional collective normal-mode coupling in quantum-dot-based bimodal microlasers

et al. 2015

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“…In the former case the atoms are localized at the maxima of the probe mode profile, attaining a maximal coupling strength, and in the latter they are localized at the minima, showing that properly positioned atoms can be nearly invisible to light circulating inside the cavity. The work presented here builds on some of our previous results [11,14,15], but the description is self-contained.…”

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Many-atom–cavity QED system with homogeneous atom–cavity coupling

et al. 2014

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We demonstrate a many-atom-cavity system with a high-finesse dual-wavelength standing wave cavity in which all participating rubidium atoms are nearly identically coupled to a 780-nm cavity mode. This homogeneous coupling is enforced by a one-dimensional optical lattice formed by the field of a 1560-nm cavity mode. OCIS codes:(020.0020) Atomic and molecular physics, (120.3940) Metrology, (140.4780) Optical resonators, (300.6260) Spectroscopy, diode lasersThere has been growing interest in collective interactions of large ensembles of atoms with cavity fields, in addition to experiments [1, 2] pursuing cavity quantum electrodynamics (cQED) with individual atoms. Topics studied include cavity-aided entanglement generation (spin squeezing) for quantum-enhanced metrology [3][4][5]; opto-mechanics with atoms, where collective motional degrees of freedom are coupled to cavity fields [6,7]; cavity-enhanced atomic quantum memories for quantum information processing [8]; and ultra-narrow-linewidth lasers using narrow-transition ultra-cold atoms as the gain medium for metrological purposes [9,10]. Important in many such systems is the inhomogeneity in the coupling strength between the participating atoms and the cavity field, which degrades the coherence of the interactions and complicates the dynamics and the analysis of the basic physics by obscuring the relevant system parameters. [11].Limiting our attention to Fabry-Pérot type cavities, in which the modes are standing waves, homogeneous coupling of atoms to the relevant cavity field (the probe mode) can be achieved by tightly trapping the atoms with a spatial period that is commensurate with the wavelength of the probe. Thus far, experimentally realized trapping configurations have involved incommensurate trap-probe periods, resulting in inhomogeneous atom-probe couplings that often require the definition of effective, averaged coupling constants [7]. Two recent efforts came to our attention that investigate commensurate dual-wavelength cavity designs; one utilizes a traveling-wave cavity to trap and probe atoms in which there is no particular atom registration [12], and the other utilizes a standing wave cavity, for the different purpose of investigating atomic self organization [13].

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“…Later, it is proved that this effect also remained for a collection of N two-level intracavity atoms [2]. At the same time, the experimental studies of the vacuum Rabi frequency were carried out in the strong coupling regime of atom and cavity [3][4][5][6][7]. Up to now, the vacuum Rabi sidebands have been developed in many regimes, such as semiconductor quantum micro-cavity with quantum wells [8], photonic crystals [9], micro-disk micro-cavity [10], and hot-atoms ensemble [11].…”

Section: Pacs Numbersmentioning

confidence: 98%

Enhanced vacuum Rabi splitting and double dark states in a composite atom-cavity system

Zhou

et al. 2009

Front. Phys. China

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The transmission spectrum of four-level atoms in a cavity is calculated. It is shown that the four separate peaks associated with normal mode splitting and intra-cavity double dark states can be observed simultaneously. The position and intensity of the four peaks can be controlled by the intensity of the third interacting light. Therefore, the enhancement of normal mode splitting by a third coupling light of the intra-cavity four-level atoms is developed.Normal mode splitting (also called vacuum Rabi splitting at the low-photo limit in an atom-cavity system) has been considered as an important effect of the quantum nature in cavity quantum electrodynamics (CQED). Eberly first predicted that the double-peak radiation spectrum of single two-level atom appeared in the presence of a cavity field [1]. Later, it is proved that this effect also remained for a collection of N two-level intracavity atoms [2]. At the same time, the experimental studies of the vacuum Rabi frequency were carried out in the strong coupling regime of atom and cavity [3][4][5][6][7]. Up to now, the vacuum Rabi sidebands have been developed in many regimes, such as semiconductor quantum micro-cavity with quantum wells [8], photonic crystals [9], micro-disk micro-cavity [10], and hot-atoms ensemble [11]. Recently, the three-peak radiation spectrum with two vacuum Rabi sidebands and a central peak was observed in a system consisting of an optical cavity and three-level atoms [12,13]. The observation of two distinct Rabi sidebands or "cavity polaritons" could be taken as the characteristic of the multi-atom enhanced coupling of atom-cavity, while the central peak represented the dark-state polariton as the combination of cavity and the phenomenon of electromagnetically induced transparency (EIT). Since the central peak has a smaller line-width than the natural line-width and the cavity line-width, it may be used for frequency stabilization, high-resolution spectroscopic measurements or other interesting applications such as control of optical multi-stability [14,15].In this paper, we present an analysis of the transmission spectrum of a cavity with four-level atoms; four transmission peaks with two Rabi sidebands and double central peaks are obtained. Different from previous theories and experiments, the third control laser is applied in addition to coupling and probe laser, which results in the enhanced Rabi splitting and two intra-cavity dark states. This paper is structured as follows. First, we calculate the nonlinear susceptibility of a homogenouslybroadened medium of four-level atoms. Second, we qualitatively discuss the properties of Rabi sidebands and double intra-cavity dark states and make a comparison when the control laser is on or off.Considering a homogeneously broadened medium inside an optical cavity, the four-level (upper levels |a and |d , lower levels |b and |c ) N-type atomic system is shown in Fig. 1. The level |a and |b are coupled by a probe field of frequency ν p with Rabi frequency Ω p and detuning Δ p = ω ab − ν p , the l...

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Normal-mode splitting with large collective cooperativity

Cited by 53 publications

References 28 publications

Unconventional collective normal-mode coupling in quantum-dot-based bimodal microlasers

Unconventional collective normal-mode coupling in quantum-dot-based bimodal microlasers

Many-atom–cavity QED system with homogeneous atom–cavity coupling

Enhanced vacuum Rabi splitting and double dark states in a composite atom-cavity system

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