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Using an evolutionary algorithm combined with a gradient descent method we design optical cavities with significantly enhanced strong coupling rates between cavity photons and a single quantum emitter. Our approach allows us to find specially designed non-spherical mirrors which lead to high-finesse cavity eigenmodes with large field enhancement at the center of the cavity. The method is based on adding consecutive perturbations to an initial spherical mirror shape using the gradient descent method for optimization. We present mirror profiles suitable for fabrication which demonstrate higher cavity cooperativity than any spherical cavity of the same size. Finally, we demonstrate numerically how such a cavity enhances the operation frequency and purity of coupling a Ca$^+$ ion to an optical fiber photon.

In a continuous measurement scheme a spin-1/2 particle can be measured and simultaneously driven by an external resonant signal. When the driving is weak, it does not prevent the particle wave-function from collapsing and a detector randomly outputs two responses corresponding to the states of the particle. In contrast, when driving is strong, the detector returns a single response corresponding to the mean of the two single-state responses. This situation is similar to a motional averaging, observed in nuclear magnetic resonance spectroscopy. We study such quantum system, being periodically driven and probed, which consists of a qubit coupled to a quantum resonator. It is demonstrated that the transmission through the resonator is defined by the interplay between driving strength, qubit dissipation, and resonator linewidth. We demonstrate that our experimental results are in good agreement with numerical and analytical calculations., Comment: 7 pages, 4 figues

We study theoretically dynamics of a driven-dissipative qubit-resonator system. Specifically, a transmon qubit is coupled to a transmission-line resonator; this system is considered to be probed via a resonator, by means of either continuous or pulsed measurements. Analytical results obtained in the semiclassical approximation are compared with calculations in the semi-quantum theory as well as with the previous experiments. We demonstrate that the temperature dependence of the resonator frequency shift can be used for the system thermometry and that the dynamics, displaying pinched-hysteretic curve, can be useful for realization of memory devices, the quantum memcapacitors., Comment: 11 pages, 9 figures

We develop a two-dimensional stochastic dissipative theory for the description of the transport of exciton polaritons accounting for their interaction with the environment of acoustic phonons. Our approach is based on the explicit modeling of the corresponding microscopic processes using a Monte Carlo framework rather than modeling from phenomenological principles. We show the dynamic formation of a condensate and investigate its characteristics, including threshold-like behavior in populations and the formation of spatial and temporal coherence at different temperatures of the environment and accounting for the stimulated nonlinear scattering, caused by system-environment interaction. The spatial coherence reveals a transition from an exponential to polynomial decay which can be attributed to the Berezinskii-Kosterlitzh-Thouless-like phase.

We study Frenkel exciton-polariton Bose-Einstein condensation in a two-dimensional defect-free triangular photonic crystal with an organic semiconductor active medium containing bound excitons with dipole moments oriented perpendicular to the layers. We find photonic Bloch modes of the structure and consider their strong coupling regime with the excitonic component. Using the Gross- Pitaevskii equation for exciton polaritons and the Boltzmann equation for the external exciton reservoir, we demonstrate the formation of condensate at the points in reciprocal space where photon group velocity equals zero. Further, we demonstrate condensation at non-zero momentum states for TM-polarized photons in the case of a system with incoherent pumping, and show that the condensation threshold varies for different points in the reciprocal space, controlled by detuning., Comment: 6 pages, 4 figures

We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"{u}ckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"{u}ckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.

We study the dynamics of a qubit-resonator system, when the resonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consider in terms of the qubit dressed states. Interaction of the dressed qubit with the second probing signal can essentially change the amplitude of this signal. We calculate the transmission amplitude of the probe signal through the resonator as a function of the qubit's energy and the driving frequency detuning. The regions of increase and attenuation of the transmitted signal are calculated and demonstrated graphically. We present the influence of the signal parameters on the value of the amplification, and discuss the values of the qubit-resonator system parameters for an optimal amplification and attenuation of the weak probe signal., Comment: 7 pages, 8 figures

We consider exciton polaritons in a semiconductor microcavity with a saturable absorber in the growth direction of the heterostructure. This feature promotes additional nonlinear losses of the system with the emergence of bistability of the condensate particles number on the nonresonant (electrical or optical) excitation intensity. Further we demonstrate a new type of bright spatial dissipative exciton-polariton soliton which emerges in the equilibrium between the regions with different particle density. We develop protocols of soliton creation and destruction. The switch to a soliton-like behavior occurs if the cavity is exposed by a short strong laser pulse with certain energy and duration. We estimate the characteristic times of soliton switch on and off and the time of return to the initial cycle. In particular, we demonstrate surprising narrowing of the spatial profile of the soliton and its vanishing at certain temperature due to interaction of the system with the thermal bath of acoustic phonons. We also address the role of polariton-polariton interaction (Kerr-like nonlinearity) on formation of dissipative solitons and show that the soliton may exist both in its presence and absence., Comment: Manuscript: 9 pages, 8 figures, published in Phys. Rev. B 92, 075305 (2015)

We analyse a system composed of a qubit coupled to electromagnetic fields of two high quality quantum oscillators. Particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. One strong signal is used for exciting the system to a high energetic state while the second weak signal is applied for probing effective eigenstates of the system. We demonstrate that a description of the system dynamics as doubly dressed qubit is applicable. Experiments show that in the case of high quality resonators the energy levels and the resonance conditions can be probed even for high driving amplitudes. The interaction of the qubit with photons of two harmonics has prospects to be used as a quantum amplifier or an attenuator., Comment: 10 pages, 3 figures

We prove, that every connected graph with $s$ vertices of degree 3 and $t$ vertices of degree at least~4 has a spanning tree with at least ${2\over 5}t +{1\over 5}s+\alpha$ leaves, where $\alpha \ge {8\over 5}$. Moreover, $\alpha \ge 2$ for all graphs besides three exclusions. All exclusion are regular graphs of degree~4, they are explicitly described in the paper. We present infinite series of graphs, containing only vertices of degrees~3 and~4, for which the maximal number of leaves in a spanning tree is equal for ${2\over 5}t +{1\over 5}s+2$. Therefore we prove that our bound is tight., Comment: 33 pages, 15 figures