Dynamical Casimir Effect Research Articles

Photon Production from the Vacuum Close to the Superradiant Transition: Linking the Dynamical Casimir Effect to the Kibble-Zurek Mechanism

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

Approximate analytical results on the cavity dynamical Casimir effect in the presence of a two-level atom

We analytically study the photon generation from vacuum due to the dynamical Casimir effect in a cavity with a two-level atom, initially prepared in an arbitrary pure state. Performing small unitary transformations, we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant and dispersive regimes.

Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.

QUANTUM-CIRCUIT ANALOG OF THE DYNAMICAL CASIMIR EFFECT AT FINITE TEMPERATURES

We proposed a quantum-circuit analog of dynamical Casimir effect by using a superconducting quantum circuit. The proposed system can be regarded as a time-dependent harmonic oscillator, resulting in squeezing of a quantum flux trapped in the system. Here we develop our theory taking into account finite temperatures, in order to contact with experiments like circuit-QED. We present numerical results of occupation probability distributions produced by non-stationary boundary effect at various temperatures.

Quantum circuit analog of the dynamical Casimir effect

We investigate a quantum-circuit analog of the dynamical Casimir effect discussed in cavity quantum electrodynamics (QED). A double superconducting quantum interference device (SQUID), consisting of a superconducting loop interrupted by a dc-SQUID, is regarded as a harmonic oscillator with a time-dependent frequency imitating the nonadiabatic boundaries in a cavity QED. Squeezing occurs due to parametric processes inherent in the system. We reformulate squeezing based on the Bogoliubov transformation between eigenstates at different times and derive the analytic formula for quantum-state evolutions of the system. The squeezing parameter clearly reveals the relationship between squeezing and nonadiabatic nature of the system. Thus, the squeezing parameter serves as a measure for the dynamical Casimir effect. We demonstrate squeezing for two types of frequency modulation and propose a method for measuring squeezing by using a circuit QED technique under coherent oscillations between an artificial atom and an LC circuit in the presence of dissipation. These observations suggest that a quantum circuit with a Josephson junction is a promising candidate for detecting the dynamical Casimir effect.

Analytical and numerical analysis of the atom–field dynamics in non-stationary cavity QED

We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field–atom coupling on the photon generation from vacuum via the dynamical Casimir effect.

Observation of the dynamical Casimir effect in a superconducting circuit

One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. Although initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences--for instance, producing the Lamb shift of atomic spectra and modifying the magnetic moment of the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed whether it might be possible to more directly observe the virtual particles that compose the quantum vacuum. Forty years ago, it was suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. The phenomenon, later termed the dynamical Casimir effect, has not been demonstrated previously. Here we observe the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of light) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detect two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.

Shaking photons out of the vacuum

The dynamical Casimir effect — the generation of photons out of the quantum vacuum induced by an accelerated body — has been experimentally demonstrated using a superconducting circuit that simulates a moving mirror. See Letter p.376 Two mirrors held parallel to each other in a vacuum experience an attractive force, known as the Casimir effect, which combines aspects of quantum vacuum behaviour with relativity. The force arises when vacuum fluctuations — virtual particles flitting in and out of existence — reduce the radiation pressure between the plates and generate an inward force. The static effect has been well studied, but theory also predicts a dynamical Casimir effect arising from a mismatch of vacuum modes in time rather than space. This paper presents the first observation of this phenomenon in a superconducting circuit.

Strong modifications of the field statistics in the cavity dynamical Casimir effect due to the interaction with two-level atoms and detectors

We study numerically the evolution of the cavity electromagnetic field mode which is in resonance with an oscillating boundary (dynamical Casimir effect), taking into account the interaction between the field and a two-level atom, that may or not be continuously monitored by a coupled atomic excitation detector. We analyze the behavior of the field statistics and the quadrature squeezing properties in different regimes, demonstrating that at the expense of decreasing the number of produced photons and the degree of squeezing, one can create qualitatively new types of cavity field states.

Quantum radiation in time-dependent dielectric media

We present a Gupta–Bleuler quantization scheme for the electromagnetic field in time-dependent dielectric media. Starting from the Maxwell equations, a generalization of the Lorentz gauge condition adapted to time-varying dielectrics is derived. Using this gauge, a Gupta–Bleuler approach to quantize all polarizations of the radiation field and the corresponding constraint condition are introduced. In this case, the contributions of unphysical photons created from vacuum cannot be thoroughly eliminated, which further results in a surface charge density. Finally, a discussion of potential experimental tests is also made, which provides another possible way to detect the dynamical Casimir effect.

Time refraction and the perturbed quantum vacuum

We discuss the classical and quantum theory of time refraction in a generic nonstationary medium. The classical description is based on temporal Fresnel and Snell’s formulas, which are similar and in some sense symmetric from their spatial counterparts. Temporal mirror effects are considered. The quantum formulation of time refraction is based on time-dependent Bogoliubov transforms, describing the evolution of the creation and destruction field operators. Photon pair creation and the associated entanglement properties are discussed. The influence of boundary conditions, the connection of time refraction with the dynamic Casimir effect, and radiation from superluminal non-accelerated optical boundaries are also discussed.

Simple model for the dynamical Casimir effect for a static mirror with time-dependent properties

We consider a real massless scalar field in 1+1 dimensions satisfying time-dependent Robin boundary condition at a static wall. This condition can simulate moving reflecting mirrors whose motions are determined by the time-dependence of the Robin parameter. We show that particles can be created from vacuum, characterizing in this way a dynamical Casimir effect.

Quantum dissipative effects in moving imperfect mirrors: Sidewise and normal motions

We extend our previous work on the functional approach to the dynamical Casimir effect, to compute dissipative effects due to the relative motion of two flat, parallel, imperfect mirrors in vacuum. The interaction between the internal degrees of freedom of the mirrors and the vacuum field is modeled with a nonlocal term in the vacuum field action. We consider two different situations: either the motion is `normal', i.e., the mirrors advance or recede changing the distance $a(t)$ between them; or it is `parallel', namely, $a$ remains constant, but there is a relative sliding motion of the mirrors' planes. For the latter, we show explicitly that there is a non-vanishing frictional force, even for a constant shifting speed.

The Dynamical Casimir Effect versus Collective Excitations in Atom Ensemble

The Dynamical Casimir effect and collective excitations in atom ensemble are investigated in a non-stationary cavity. The results show that the dynamical Casimir effect leads to the collective excitations of atom ensemble due to absorption of the created photons. This remarkable feature indicates that the atom ensemble can serve as a detector for the process of photon production in a non-stationary cavity. Therefore by measuring the collective excitations of the atom ensemble, the dynamical Casimir effect can indirectly be verified.

The influence of temporal coherence on the dynamical Casimir effect

We study the dynamical Casimir effect in the presence of a finite coherence time, which is associated with a finite quality factor of the optical cavity. We use the time refraction model, where a fixed cavity with a modulated optical medium, replaces the empty cavity with a vibrating mirror. Temporal coherence is described with the help of cavity quasi-mode operators. Asymptotic expressions for the number of photon pairs generated from vacuum are derived.

A Re-Entrant ${\hbox{MgB}}_{2}$ Cavity for Dynamic Casimir Experiment

The use of radio frequencies (RF) superconducting re-entrant cavities has been suggested in the framework of some research to detect photon generation from the vacuum, due to the dynamical Casimir effect. A thin semiconducting slab, put inside the cavity, will be excited by a train of laser pulses of a frequency twice the resonant frequency of the cavity, so that a periodic modulation of the dielectric constant of the slab will be realized. In order to produce a RF cavity that can safely work at temperatures larger than 4 K, we have designed and constructed a MgB2 re-entrant cavity having a resonant frequency in the range of 2-3 GHz. The cavity is made by a cylindrical cup of about 40 mm of internal diameter and 40 mm of height and on its base is standing a cylindrical coaxial nose on which the semiconductor slab will be deposited. The details of the construction of the MgB2 cavity will be presented as well as the measurements of its quality factor, as a function of the temperature.

Parametric amplification of the classical field in cavities with photoexcited semiconductors

A model describing the parametric amplification of a classical signal in an electromagnetic high-Q cavity containing a periodically illuminated thin semiconductor slab is presented. This model can be useful for the interpretation of the results of the so-called ‘MIR’ experiment aimed at the observation of the dynamical Casimir effect.

Photon creation in a resonant cavity with a nonstationary plasma mirror and its detection with Rydberg atoms

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 excitations is examined through the atom-field interaction. Some consideration is made for a feasible experimental realization with a semiconductor plasma mirror.

Photon Generation in an Electromagnetic Cavity with a Time-Dependent Boundary

We report the observation of photon generation in a microwave cavity with a time-dependent boundary condition. Our system is a microfabricated quarter-wave coplanar waveguide cavity. The electrical length of the cavity is varied by using the tunable inductance of a superconducting quantum interference device. It is measured at a temperature significantly less than the resonance frequency. When the length is modulated at approximately twice the static resonance frequency, spontaneous parametric oscillations of the cavity field are observed. Time-resolved measurements of the dynamical state of the cavity show multiple stable states. The behavior is well described by theory. Our results may be considered a preliminary step towards demonstrating the dynamical Casimir effect.

Dynamical Casimir effect in superconducting microwave circuits

We theoretically investigate the dynamical Casimir effect (DCE) in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose implementing a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum-interference devices that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free space. We analyze the properties of the DCE in these two setups by calculating the generated photon-flux densities, output-field correlation functions, and the quadrature squeezing spectra. We show that these properties of the output field exhibit signatures unique to the radiation due to the DCE, and could, therefore, be used for distinguishing the DCE from other types of radiation in these circuits. We also discuss the similarities and differences between the DCE, in the resonator setup, and the down-conversion of pump photons in parametric oscillators.