We study theoretically the nonstationary circuit QED system in which the artificial atom transition frequency, or the atom-cavity coupling, have a small periodic time modulation, prescribed externally. The system formed by the atom coupled to a single cavity mode is described by the Rabi Hamiltonian. We show that, in the dispersive regime, when the modulation periodicity is tuned to the `resonances', the system dynamics presents the dynamical Casimir effect, resonant Jaynes-Cummings or resonant Anti-Jaynes-Cummings behaviors, and it can be described by the corresponding effective Hamiltonians. In the resonant atom-cavity regime and under the resonant modulation, the dynamics is similar to the one occurring for a stationary two-level atom in a vibrating cavity, and an entangled state with two photons can be created from vacuum. Moreover, we consider the situation in which the atom-cavity coupling, the atomic frequency, or both have a small nonperiodic time modulation, and show that photons can be created from vacuum in the dispersive regime. Therefore, an analog of the dynamical Casimir effect can be simulated in circuit QED, and several photons, as well as entangled states, can be generated from vacuum due to the anti-rotating term in the Rabi Hamiltonian.
We show a quantum boost in the output power of a heat engine formed by a two-level system coupled to a single-mode cavity. The key ingredient here is the nonstationary regime achieved when some system parameter (atomic transition frequency, in our case) is subjected to a time-dependent perturbative modulation that is precisely tuned at certain frequencies. We discuss how the extracted power can lead to amplification of the external driving field. Quantum power boost is found both in the nonstationary Jaynes-Cummings and Rabi models, indicating that our predictions can be experimentally tested …
We investigate analytically and numerically the nonstationary circuit QED setup in which $N$ independent qubits interact with a single mode of the Electromagnetic field confined in a resonator. We consider the harmonic time modulation of some parameter (atomic transition frequency or the atom-field coupling strength) and derive the unitary dynamics up to the second order in the modulation depth for $N=1$ and $N\gg 1$. It is shown that all the resonant phenomena that occur for modulation frequencies $\sim 2ω_{0}$ (where $ω_{0}$ is the cavity frequency) also occur for the halved frequencies. How…
We investigate the dynamical Casimir effect and its detection with Rydberg atoms. The photons are created in a resonant cavity with a plasma mirror of a semiconductor slab which is irradiated by periodic laser pulses. The canonical Hamiltonian is derived for the creation and annihilation operators showing the explicit time-variation in the couplings, which originates from the external configuration such as a nonstationary plasma mirror. The number of created photons is evaluated as squeezing from the Heisenberg equations with the Hamiltonian. Then, the detection of the photons as the atomic ex…
Invariant creation and annihilation operators and related Fock states and coherent states are built up for the system of nonstationary fermionic forced oscillator.
The most general form of Hamiltonian that preserves fermionic coherent states stable in time is found in the form of nonstationary fermion oscillator. Invariant creation and annihilation operators and related Fock states and coherent states are built up for the more general system of nonstationary forced fermion oscillator.
We consider the nonstationary circuit QED setup in which a 3-level artificial atom in the $Δ$-configuration interacts with a single-mode cavity field of natural frequency $ω$. It is demonstrated that when some atomic energy level(s) undergoes a weak harmonic modulation, photons can be generated from vacuum via effective 1- and 3-photon transitions, while the atom remains approximately in the ground state. These phenomena occur in the dispersive regime when the modulation frequency is accurately tuned near $ω$ and $3ω$, respectively, and the generated field states exhibit strikingly different s…
In the solid-state circuit QED system and based on the homodyne measurement in dispersive regime, we demonstrate that a homodyne-current-based feedback can create and stabilize highly entangled two-qubit states in the presence of moderate noisy environment. Particularly, we present an extended analysis for the current-based Markovian feedback, which leads to an improved filtered-current-based feedback scheme. We show that this is essential for us to achieve the desirable control effect in present system.
We consider an analog of particle production in a quartic $O(N)$ quantum oscillator with time-dependent frequency, which is a toy model of particle production in the dynamical Casimir effect and de Sitter space. We calculate exact quantum averages, Keldysh propagator, and particle number using two different methods. First, we employ a kind of rotating wave approximation to estimate these quantities for small deviations from stationarity. Second, we extend these results to arbitrarily large deviations using the Schwinger-Keldysh diagrammatic technique. We show that in strongly nonstationary sit…
We consider the nonstationary circuit QED architecture, where a single artificial two-level atom interacts with a cavity field mode under external modulation of one or more system parameters. Two different approaches are employed to study the effects of Markovian dissipation on modulation-induced transitions between the atom-field dressed states: the standard master equation of Quantum Optics and the recently formulated dressed-picture master equation. We estimate the associated transition rates and show that photon generation from vacuum ("dynamical Casimir effect", DCE) and coherent photon a…
We study the peculiarities of the nonstationary Casimir effect (creation of photons in cavities with moving boundaries) in the special case of two resonantly coupled modes with frequencies $ω_0$ and $(3Δ)ω_0$, parametrically excited due to small amplitude oscillations of the ideal cavity wall at the frequency $2ω_0(1δ)$ (with $|δ|,|Δ|\ll 1$). The effects of thermally induced oscillations in time dependences of the mean numbers of created photons and the exchange of quantum purities between the modes are discovered. Squeezing and photon distributions in each modes are calculated for initial vac…
Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy…
We present a method to engineer the unitary charge conjugation operator, as given by quantum field theory, in the highly controlled context of quantum optics, thus allowing one to simulate the creation of charged particles with well-defined momenta simultaneously with their respective antiparticles. Our method relies on trapped ions driven by a laser field and interacting with a single mode of a light field in a high Q cavity.
The analytical solution of the task of the interaction of quantized EM-field with multichain quasionedimensional axially symmetric qubit system by taking into account both the intrachain and interchain qubit coupling has been obtained for the first time. The appearance of additional lines in optical spectra of quasionedimensional systems strongly interacting with EM-field is predicted. They are result of nonstationary registration conditions, to be consequence of Rabi wave packet formation and correspond to Fourier transformation of revival part of Rabi wave packets in temporal dependence of t…
Spin correlations of $e^{+}e^{-}$ pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be \textit{energy} (speed) dependent, for initially \textit{linearly} and \textit{circularly polarized} photons, different from those obtained by simply combining the spins of the relevant particles, for initially \textit{polarized} photons. These expressions also depend on the angles of spin of $e^{+}$ (and/or of $e^{-}$), for initially {\it linearly polarized} photons, but not for {\it circularly polarized} photon…
One of the fundamental predictions of Quantum Electrodynamics (QED) is the spontaneous creation of particle--antiparticle pairs from vacuum in presence of a very strong electric field. Under these extreme conditions a strongly bound state can fetch an otherwise unobservable electron from the Dirac sea, leaving behind a hole representing a positron. Although generally known for many decades, the effect has not yet been demonstrated experimentally. We propose an analogue model of the quantum Dirac field, realized by ultra--cold fermionic atoms in an optical lattice, aiming at an experimental sim…
We consider the nonstationary circuit QED architecture in which a single-mode cavity interacts with N>1 identical qubits, and some system parameters undergo a weak external perturbation. It is shown that in the dispersive regime one can engineer the two-photon exchange interaction by adjusting the frequency of harmonic modulation to (approximately) $2|Δ_{-}|$, where $Δ_{-}$ is the average atom--field detuning. Closed analytic description is derived for the weak atom-field coupling regime, and numeric simulations indicate that the phenomenon can be observed in the present setups.
The Rabi Hamiltonian describes the interaction between a two-level atom and a single mode of the quantized electromagnetic field. When the system is subject to the Markovian atomic dephasing reservoir, the anti-rotating term leads to the photon generation from vacuum. In the presence of Markovian damping reservoirs, the asymptotic mean photon number is higher than the thermal photon number expected in the absence of the anti-rotating term. We obtain approximate analytical expressions in the asymptotic regime for the photon creation rate in the pure dephasing case and the mean photon number and…
We study a qubit undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the qubit, being independent of the frequency of the QED mode. Possible applications are single-photon generation and the controllable creation of qubit-oscillator entanglement.
Sign-changing interactions constitute a crucial ingredient in the creation of frustrated many-body systems such as spin glasses. We present here the demonstration of a photon-mediated sign-changing interaction between Bose-Einstein condensed (BEC) atoms in a confocal cavity. The interaction between two atoms is of an unusual, nonlocal form proportional to the cosine of the inner product of the atoms' position vectors. This interaction arises from the differing Gouy phase shifts of the cavity's degenerate modes. Moreover, these Gouy phase anomalies induce an extra pattern of Z_2-symmetry-breaki…
We present a way to create entangled states of two superconducting transmon qutrits based on circuit QED. Here, a qutrit refers to a three-level quantum system. Since only resonant interaction is employed, the entanglement creation can be completed within a short time. The degree of entanglement for the prepared entangled state can be controlled by varying the weight factors of the initial state of one qutrit, which allows the prepared entangled state to change from a partially entangled state to a maximally entangled state. Because a single cavity is used, only resonant interaction is employe…
With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an efficient operating regime. Using state-of-the-art quantum optimal control techniques, we exhaustively explore the landscape for creation and removal of entanglement over a wide range of design parameters. We identify an optimal operating region outside of the usually considered strongly dispersive regime, where multiple sources of entanglement interfere simultaneo…
We propose a scheme to realize a multiqubit tunable phase gate in a circuit QED setup where two resonators, each coupling with a qudit, are interconnected to a common qudit (d=4). In this proposal, only two levels of each qudit serve as the logical states and the other two levels are used for the gate realization. The proposal is efficient and simple because only a classical microwave pulse is needed, no matter how many qudits are involved, which significantly reduces experimental difficulty. In a nonresonant case, the tunable phase gate can be achieved readily, while under the resonant condit…
We solve the Jaynes-Cummings Hamiltonian with time-dependent coupling parameters under dipole and rotating-wave approximation for a three-dimensional (3D) photonic crystal (PC) single mode cavity with a sufficiently high quality (Q) factor. We then exploit the results to show how to create a maximally entangled state of two atoms, and how to implement several quantum logic gates: a dual-rail Hadamard gate, a dual-rail NOT gate, and a SWAP gate. The atoms in all of these operations are syncronized, which is not the case in previous studies [1,2] in PCs. Our method has the potential for extensio…
Quantum mechanical effects at the macroscopic level were first explored in Josephson junction-based superconducting circuits in the 1980's. In the last twenty years, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review.…
To generate a NOON state with a large photon number $N$, the number of operational steps could be large and the fidelity will decrease rapidly with $N$. Here we propose a method to generate a new type of quantum entangled states, $(|NN00\rangle+|00NN\rangle)/\sqrt{2}$ called "double NOON" states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process, i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a con…
The realization of cross-Kerr nonlinearity is an important task for many applications in quantum information processing. In this work, we propose a method for realizing cross-Kerr nonlinearity interaction between two superconducting coplanar waveguide resonators coupled by a three-level superconducting flux qutrit (coupler). By employing the qutrit-resonator dispersive interaction, we derive an effective Hamiltonian involving two-photon number operators and a coupler operator. This Hamiltonian can be used to describe a cross-Kerr nonlinearity interaction between two resonators when the coupler…
Within the theory of vacuum creation of an $e^{+}e^{-}$ - plasma in the strong electric fields acting in the focal spot of counter-propagating laser beams we compare predictions on the basis of different WKB-type approximations with results obtained in the framework of a strict kinetic approach. Such a comparison demonstrates a considerable divergence results. We analyse some reasoning for this observation and conclude that WKB-type approximations have an insufficient foundation for QED in strong nonstationary fields. The results obtained in this work on the basis of the kinetic approach are m…
We develop a microscopic toy model for Cavity dynamical Casimir effect (DCE), namely, the photon generation from vacuum due to a nonstationary dielectric slab in a fixed single mode cavity. We represent the slab by $N\gg 1$ noninteracting two-level atoms coupled to the field via the standard dipole interaction. We show that the DCE is contained implicitly in the light-matter interaction Hamiltonian when its parameters are externally prescribed functions of time. We also predict several new phenomena, such as saturation of the photon growth due to effective Kerr nonlinearity, generation of pair…
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of low rate can be expanded into small shift errors. The qubit space is defined as an eigenspace of two mutually commuting displacement operators $S_p$ and $S_q$ which act as large shifts/translations in phase space. We propose and analyze the approximate creation of these qubit states by coupling the oscillator to a sequence of ancilla qubits. This preparation o…
We investigate the degree of entanglement between an atom and a driven cavity mode, in the presence of dissipation. Previous work has shown that in the limit of weak driving fields, the steady state entanglement is proportional to the square of the driving intensity. This quadratic dependence is due to the generation of entanglement by the creation of pairs of photons/excitations. In this work we investigate the entanglement between an atom and a cavity in the presence of multiple photons. Nonlinearity of the atomic response is needed to generate entanglement, but as that nonlinearity saturate…
We introduce a systematic formalism for two-resonator circuit QED, where two on-chip microwave resonators are simultaneously coupled to one superconducting qubit. Within this framework, we demonstrate that the qubit can function as a quantum switch between the two resonators, which are assumed to be originally independent. In this three-circuit network, the qubit mediates a geometric second-order circuit interaction between the otherwise decoupled resonators. In the dispersive regime, it also gives rise to a dynamic second-order perturbative interaction. The geometric and dynamic coupling stre…
A relativistic quantum mechanics is formulated in which all of the interactions are in the four-momentum operator and Lorentz transformations are kinematic. Interactions are introduced through vertices, which are bilinear in fermion and antifermion creation and annihilation operators, and linear in boson creation and annihilation operators. The fermion-antifermion operators generate a unitary Lie algebra, whose representations are fixed by a first order Casimir operator (corresponding to baryon number or charge). Eigenvectors and eigenvalues of the four-momentum operator are analyzed and exact…
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations. In the single excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the…
Superconducting circuits provide a new platform to study nonstationary cavity QED phenomena. An example of such a phenomenon is a dynamical Lamb effect which is a parametric excitation of an atom due to the nonadiabatic modulation of its Lamb shift. This effect has been initially introduced for a natural atom in a varying cavity, while we suggested its realization in a superconducting qubit-cavity system with dynamically tunable coupling. In the present paper, we study the interplay between the dynamical Lamb effect and the energy dissipation, which is unavoidable in realistic systems. We find…
