We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta $J_{g}$ and $J_{e}$ of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broad-band radiation is given. We indicate various applications of these results.
We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time-propagation of an arbitrary initial state is developed, based on a series of transformations thereby removing the time-dependence of the boundary conditions. The time-evolution of the energies of different initial states is studied. The maximal and minimal energy that is reached during the time-evolution shows a series of resonances as a function of the applied driving frequency. At these resonances, higher (or lower) lying states are periodic…
A Fermi's Golden Rule for population transfer between instantaneous eigenstates of elliptical quantum billiards with oscillating boundaries is derived. Thereby, both the occurrence of the recently observed resonant population transfer between instantaneous eigenstates [F. Lenz et al. New J. Phys., {\bf 13}, 103019, 2011] and the empirical criterion stating that these transitions occur when the driving frequency matches the mean difference of the latter are explained. As a second main result a criterion judging which resonances are resolvable in a corresponding experiment of certain duration is…
We systematically investigate possible helix states in XXZ Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction. Exact solutions show that a set of precession helix states can be constructed by deliberate superposition of degenerate eigenstates of the Hamiltonian under the resonant condition. When a non-Hermitian balance boundary term is imposed as a quenching action, the quench dynamics shows that a steady helix state emerges from some easily prepared initial states, including saturate and maximally mixed ferromagnetic states, according to the analysis of perturbation method. The corr…
We present a numerical study of the resonant high harmonic generation by tin ions in an elliptically-polarised laser field along with a simple analytical model revealing the mechanism and main features of this process. We show that the yield of the resonant harmonics behaves anomalously with the fundamental field ellipticity, namely the drop of the resonant harmonic intensity with the fundamental ellipticity is much slower than for high harmonics generated through the nonresonant mechanism. Moreover, we study the polarisation properties of high harmonics generated in elliptically-polarised fie…
Oscillations in time-dependent 2D electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state, so the relevance of these arguments to the natural process is unclear. Here we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. It is found that vibrations resonant with the energy difference between exciton states do not increase the quantum y…
We report a theoretical study of the electromagnetic waves (EWs) propagation through an array of superconducting qubits, i.e. coherent two-level systems, embedded in a low-dissipative transmission line. We focus on the near-resonant case as the frequency of EWs $ω\simeq ω_q$, where $ω_q$ is the qubit frequency. In this limit we derive the effective dynamic nonlinear wave equation allowing one to obtain the frequency dependent transmission coefficient of EWs, $D(ω)$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D(ω)$ in both cases of a …
We study resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential which suppresses simultaneous excitation of neighboring atoms. Considering two- and three-level excitation schemes, we analyze the dynamics and stationary state of the continuously-driven, dissipative many-body system employing time-dependent density-matrix renormalization group (t-DMRG) simulations. We show that two-level atoms can exhibit only nearest neighbor correlations, while three-level atoms under dark-state resonant driving can develop finite-ra…
We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such dynamics: 1) the collapse and revival of oscillations in the population difference, 2) the simple exponential decay of the oscillations resulting in their steady state with the finite amplitude, and 3) the steady-state stabilization of the equally populated levels. The nonmonotonic Bessel-function-like dependence on the driving strength is also predicted for th…
We propose a dissipative method for preparation of a maximally entangled steady state of two trapped ions in the Lamb-Dicke limit. By addressing the trapped-ion system with a monochromatic standing wave laser pulse of frequency resonant with the ionic transition and a microwave field coupled to the ground-state transitions, we obtain an effective coupling between two particles, which is independent of the phonon-number fluctuations. Meanwhile, the controlled spontaneous emission of trapped ions is implemented via pumping the metastable states upwards to the short-lived ionic states by an auxil…
We study the steady state of two coupled two-level atoms interacting with a non-equilibrium environment that consists of two heat baths at different temperatures. Specifically, we analyze four cases with respect to the configuration about the interactions between atoms and heat baths. Using secular approximation, the conventional master equation usually neglects steady-state coherence, even when the system is coupled with a non-equilibrium environment. When employing the master equation with no secular approximation, we find that the system coherence in our model, denoted by the off-diagonal t…
Steady-State Emission of Quantum-Correlated Light in the Telecom Band from a Single Atom
Te Whai Ao–Dodd-Walls Centre for Photonic and Quantum Technologies（Te Whai Ao–Dodd-Walls 光子与量子技术中心）；Department of Physics, University of Auckland（奥克兰大学物理系）；Department of Applied Physics, Waseda University（早稻田大学应用物理系）
We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Walls interaction range with perspectives for entangling large and distant ensembles.
The key challenge to scalable optical quantum computing, boson sampling, and quantum metrology is sources of single photons with near-unity system efficiency and simultaneously near-perfect indistinguishability in all degrees of freedom (including spectral, temporal, spatial, and polarization). However, previous high-indistinguishability solid-state single-photon sources had to rely on polarization filtering that reduced the system efficiency by at least 50%. Here, we overcome this challenge by developing a new single-photon source based on a coherently driven quantum dot embedded in an ellipt…
The coherent dynamics of relaxing spin qubits driven by a classical bichromatic field comprising a strong resonant component and a weaker component with a frequency close to the strong-field Rabi frequency is studied. The double dressing by the bichromatic field modifies dephasing and dissipation processes. We demonstrate that detuning of the weaker-field frequency from the strong-field Rabi frequency prolongs the decay of Rabi oscillations between some doubly dressed states. The sensitivity of Rabi oscillations to the modified detuning-dependent relaxation is illustrated for nitrogen-vacancy …
We consider the influence of the near dipole-dipole interaction, underlying the local field, on the dynamics of two-level and V-type three-level atoms exposed to cw-laser radiation. The dipole-dipole interaction between the V-type three-level atoms is shown to give rise to the Poincaré-Andronov-Hopf bifurcation in steady-state solution of the equations of motion. As a result, the populations of the energy levels periodically vary in time. In the framework of the two-level model, dynamical instabilities are proved to be impossible.
The control of light transmission through a Fabry-Perot cavity containing atoms is theoretically investigated, when the cavity mode beam and an intersecting control beam are both close to specific atomic resonances. A four-level atomic system is considered and its interaction with the cavity mode is studied by solving for the time dependent cavity field and atomic state populations. The conditions for optical bistability of the atom-cavity system are obtained in steady state limit. For an ensemble of atoms in the cavity mode, the response of the intra-cavity light intensity to the intersecting…
We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two parameters - detuning between the clocks and the repump rate. There are three main phases - trivial steady state (Phase I), where all atoms are maximally pumped, nontrivial steady state corresponding to monochromatic superradiance (Phase II), and amplitude-modulated superradiance (Phase III). Phases I and II are fixed points of the mean-field dynamics, wh…
We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P-representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the mu…
