Ultrastrong Light-Matter Coupling Regime with Polariton Dots

Todorov, Yanko; Andrews, A. M.; Colombelli, R.; Liberato, Simone De; Ciuti, Cristiano; Klang, P.; Strasser, G.; Sirtori, Carlo

doi:10.1103/physrevlett.105.196402

Cited by 406 publications

(485 citation statements)

References 20 publications

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“…Third, the symmetric coupled cavity mode couples to the symmetric exciton state ψ S , and the antisymmetric coupled cavity mode couples to the antisymmetric exciton state ψ AS via the equation which describes the eigenvalues of the Hopfield Hamiltonian of the interacting system 24,38,39 :…”

Section: Modified Four-oscillator Coupled Model For Coupled Omcsmentioning

confidence: 99%

Coupling of exciton-polaritons inlow−Qcoupled microcavities beyond the rotating wave approximation

et al. 2015

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We have demonstrated coupling between a pair of ultrastrong light-matter coupled microcavities composed of neat glassy organic dye films between metallic (silver) mirrors at room temperature. Based upon our modified coupled oscillator model, we have observed that the degeneracy between the Rabi splittings associated with the symmetric and antisymmetric cavity modes is broken by the higher-order anti-resonant terms in the Hamiltonian associated with the breakdown of the rotating wave approximation in the ultrastrong coupling regime. These results are in quantitative agreement with both experiment and transfer matrix modeling. The component cavities are characterized by Q factors around 12 and display a large vacuum Rabi splitting around 1.12 eV between the upper and lower polariton branches, which is about 52% of the excited state energy, thus indicating ultrastrong coupling in each individual cavity. This large splitting is due to the large oscillator strength of the neat dye glass. We have also observed large polariton-induced incidence-side asymmetry in reflection spectra in a coupled cavity pair with one cavity having no exciton.

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Section: Modified Four-oscillator Coupled Model For Coupled Omcsmentioning

confidence: 99%

Coupling of exciton-polaritons inlow−Qcoupled microcavities beyond the rotating wave approximation

et al. 2015

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“…Already the validity of these effective Hamiltonians and their properties can be a matter of debate [24][25][26] and often further simplifications are adopted such as the JaynesCummings model in the rotating-wave approximation. The rapid progress in quantum-optical experiments, on the other hand, especially in the field of cavity QED [27][28][29][30] and circuit QED [31,32], allows us to study and control multiparticle systems ultrastrongly coupled to photons [33][34][35][36], where such a simple approximative treatment is no longer valid [37]. This new regime of light-matter interaction is widely unexplored for, e.g., molecular physics and material sciences [38].…”

Section: Introductionmentioning

confidence: 99%

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

et al. 2014

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In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

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“…In the case of the RWA, its energy spectrum and wavefunctions can be solved exactly [2]. With the rapid development of fabricated technique in solid-state systems, the Jaynes-Cummings model can be realized in semiconducting dots [3][4][5][6] and superconducting Josephson junctions [7][8][9][10][11][12]. More importantly, recent experiment has reported the existence of the ultrastrong coupling with the ratio 0.12 between the coupling strength and the microwave photon frequency [13].…”

mentioning

confidence: 99%

Light-shift-induced quantum phase transitions of a Bose-Einstein condensate in an optical cavity

Lian

et al. 2011

Phys. Rev. A

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We present a generalized variational method to analytically obtain the ground-state properties of the unsolvable Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which can not be treated in the adiabatical approximation and the generalized rotating-wave approximation. Finally, we also demonstrate analytically how to control the mean photon number by means of the current experimental parameters including the photon frequency, the coupling strength, and especially the atomic resonant level. The Jaynes-Cummings model, which describes the important interaction between the atom and the photon of a quantized electromagnetic field, is a fundamental model in quantum optics and condensed-matter physics as well as in quantum information science. In the optical cavity quantum electrodynamics, the atom-photon coupling strength is far smaller than the photon frequency. As a result, the system dynamics can be well governed by the Jaynes-Cummings model with the rotating-wave approximation (RWA) [1]. In the case of the RWA, its energy spectrum and wavefunctions can be solved exactly [2]. With the rapid development of fabricated technique in solid-state systems, the Jaynes-Cummings model can be realized in semiconducting dots [3][4][5][6] and superconducting Josephson junctions [7][8][9][10][11][12]. More importantly, recent experiment has reported the existence of the ultrastrong coupling with the ratio 0.12 between the coupling strength and the microwave photon frequency [13]. Moreover, this ratio maybe approach unit due to the current efforts [14,15].However, in this ultrastrong coupling regime the wellknown RWA breaks down and the whole Hamiltonian is written aswhere a † and a are creation and annihilation operators for photon with frequency ω, σ ± are the raising and lowering operators of the two-level atom in the basis of σ z , Ω is the atomic resonant frequency and g is the atomphoton coupling strength. Due to the existence of the counter-rotating terms (σ + a + and σ − a), Hamiltonian (1) is very difficult to be solved analytically except for Ω = 0. Although the energy spectrum of Hamiltonian (1) has been obtained perfectly by means of the numerical simu- * Corresponding author: chengang971@163.com lation [16][17][18], the analytical solutions are very necessary for extracting the fundamental physics as well as in processing quantum information [19][20][21]. In the negative detuning Ω < ω, the adiabatic approximation method that the second term of Hamiltonian (1) is treated as a small perturbation has been considered [22]. Recently, a generalized rotating-wave approximation (GRWA) has also been proposed to solve Hamiltonian (1) in the displaced oscillator basis states [23]. This method ...

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Ultrastrong Light-Matter Coupling Regime with Polariton Dots

Cited by 406 publications

References 20 publications

Coupling of exciton-polaritons inlow−Qcoupled microcavities beyond the rotating wave approximation

Coupling of exciton-polaritons inlow−Qcoupled microcavities beyond the rotating wave approximation

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Light-shift-induced quantum phase transitions of a Bose-Einstein condensate in an optical cavity

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