Resonant Field Mode Research Articles

Entanglement of two superconducting qubits induced by a thermal noise of a cavity with Kerr medium taking into account the atomic coherence

The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

A vapor-cell atomic sensor for radio-frequency field detection using a polarization-selective field enhancement resonator

We present a hybrid atomic sensor that realizes radio-frequency electric field detection with intrinsic field enhancement and polarization selectivity for robust high-sensitivity field measurement. The sensor incorporates a passive resonator element integrated with an atomic vapor cell that provides enhancement and polarization selectivity of incident radio-frequency fields. The enhanced intra-cavity radio-frequency field is measured by atoms using a quantum-optical readout of AC level shifts of field-sensitive atomic Rydberg states. In our demonstration, we employ a split field-enhancement resonator embedded in a rubidium vapor cell to enhance and detect C-band radio-frequency fields. We observe a field enhancement equivalent to a 24 dB gain in intensity sensitivity. The spatial profile of the resonant field mode inside the field-enhancement cavity is characterized and robust polarization measurement of the incident field is demonstrated. The measured performance metrics of the sensor are in good agreement with simulations. Applications of such atomic sensors in ultra-weak radio-frequency detection and advanced measurement capabilities are discussed.

Non-equilibrium dynamics of the Dicke model for mesoscopic aggregates: signatures of superradiance

The dynamics of the Dicke model, which describes the interaction of N two-level atoms with a resonant field mode, is studied in the presence of dissipation and in strong non-equilibrium for a moderate number of atoms. Starting from a highly excited state, it is investigated to what extent signatures of superradient phenomena known from the thermodynamic limit , namely, superradiant light emission and atom-field correlations characteristic for the superradiant phase, appear on transient time scales. Attention is also paid to subtleties of modeling dissipation in the weak coupling limit and to the dynamics in phase space. The latter allows phase space correlators to be defined as indicators for collective behavior on transient time scales. These findings may be of relevance for the realization of Dicke physics with superconducting circuits.

Influence of Interaction of Two Atoms on the Dynamical Casimir Effect

We study the problem of photon creation from a vacuum in an ideal cavity with vibrating walls in the resonance case, taking into account the interaction between the resonant field mode and a detector modeled by two two-level atoms. By solving the problem in a matrix method, we obtain an analytic solution. It is shown that the interaction between two atoms has passive influence on the rate of photons creation. The larger the coupling constant between the atoms is, the fewer photons generated at the same time.

Quantum simulations of relativistic quantum physics in circuit QED

We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy–Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.

Influence of the field-detector coupling strength on the dynamical Casimir effect

We consider the problem of photon creation from a vacuum inside an ideal cavity with vibrating walls in the resonance case, taking into account the interaction between the resonant field mode and a detector modeled by a quantum harmonic oscillator. The frequency of wall vibrations is taken to be twice the cavity normal frequency, modified due to the coupling with the detector. The dynamical equations are solved with the aid of the multiple scales method. Analytical expressions are obtained for the photon mean numbers and their variances for the field and detector modes, which are supposed to be initially in the vacuum quantum states. We analyze different regimes of excitation, depending on the ratio of the modulation depth of the time-dependent cavity eigenfrequency to the coupling strength between the cavity mode and detector. We show that statistical properties of the detector quantum state (variances of the photon numbers, photon distribution function, and the degree of quadrature squeezing) can be quite different from that of the field mode. Besides, the mean number of quanta in the detector mode increases with some time delay, compared with the field mode.

Quantum optical thermodynamic machines: Lasing as relaxation

Motivated by the growing interest in the nanophysics and the field of quantum thermodynamics we study an open quantum system consisting of two spatially separated two-level atoms (spins) coupled to a quantum oscillator (resonator field mode). There is no external driving. The spins of different energy splittings are each linked to a heat bath with different temperature. We find that the temperature gradient imposed on the system together with the oscillator operating as a kind of work reservoir makes this system act as a thermodynamic machine, in particular, as a heat engine (laser). We analyze the properties of the resulting resonator field and of the engine functionality. For the latter problem we use recently developed definitions of heat flux and power as well as a test, in which the resulting field is used as an input for a heat pump.

Quantum heat engine: A fully quantized model

Motivated by the growing interest in the nanophysics and the field of quantum thermodynamics [J. Gemmer, M. Michel, G. Mahler, Springer, 2005] we study a system consisting of two different 2-level atoms (spins) coupled to a quantum oscillator (resonator field mode), and each spin linked to a heat bath with different temperatures. We find that the energy gradient imposed on the system and the “coherent driving” of the two atoms achieved by the oscillator make this system act as a thermodynamic machine. We analyze the engine dynamics using the recently developed definitions of heat flux and power [E. Boukobza, D.J. Tannor, Phys. Rev. A. 74 (2006) 063823; H. Weimer, M.J. Henrich, F. Rempp, H. Schröder, G. Mahler, Eur. Phys. Lett. 83 (3) (2008) 30008]. The system can work as heat engine (laser) or a heat pump in a non-cyclic continuous mode. We characterize the properties of the resonator field. The concept of work and heat for this machine is discussed.

Anomalous Doppler-effect and polariton-mediated cooling of two-level atoms.

We consider an atom moving in a near resonant laser field with its dipole strongly coupled to a resonator field mode. As compared to the standard Doppler shift, we find a substantially different and counterintuitive linear velocity dependence of the light scattering properties. The mechanical force of the laser field exhibits strong velocity selectivity at a polariton resonance, which gives rise to an enhanced friction force and Doppler cooling even in the directions perpendicular to the resonator axis. This effect allows for sub-Doppler cooling of atoms even with a nondegenerate ground state.

Long-term quantum treatment of the spontaneous emission of an atom interacting with a strongly populated mode

In this note we made an all quantum treatment of the long-term spontaneous emission of a two-level atom, strongly interacting with a resonant mode. The spectra of the spontaneous emission, as they arc registered either by a large-band detector or by a monochromatic one, are calculated for various times of interaction and interaction strengths. The energy levels of a two-level atom in interaction with a resonant field mode (atom plus field mode system or AFM system) are clustered into n-blocks of two levels l+>n and [-->,~ with energies h(no)o~ ~r where to o is the circular frequency of the field mode, a the coupling constant of the interaction between the atom and the mode and n the occupation number of the mode. If we call II> and ]2>, respectively, the atom ground-state and excited-state wave functions, the stationary states ]+>, and ]-->~ of the AFM system can be written (1)