The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number, n, and critical atom number, N, cannot be minimized simultaneously, so that an "optimal" sphere size is taken to be the radius for which the geometric mean, (n x N)^(1/2), is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the D2 transition in atomic Cesium (852nm) using fused-silica microspheres, for which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is minimized occurs at a=7.83microns. On an experimental front, we have fabricated fused-silica microspheres with radii a=10microns and consistently observed quality factors Q=0.8x10^(7). These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.
We study a scheme for entangling two-level atoms located close to the surface of a dielectric microsphere. The effect is based on medium-assisted spontaneous decay, rigorously taking into account dispersive and absorptive properties of the microsphere. We show that even in the weak-coupling regime, where the Markov approximation applies, entanglement up to 0.35 ebits between two atoms can be created. However, larger entanglement and violation of Bell's inequality can only be achieved in the strong-coupling regime.
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the surface-guided field resonances inside the gap (for a dielectric or a metallic sphere) are considered. Since the decay rate mimics the spectral density of the sphere-assisted ground-state fluctuation of the radiation field, the strengths and widths of the field resonances essenti…
We propose a scheme to realize quantum controlled phase flip (CPF) between two rare earth ions embedded in respective microsphere cavity via interacting with a single-photon pulse in sequence. The numerical simulations illuminate that the CPF gate between ions is robust and scalable with extremely high fidelity and low error rate. Our scheme is more applicable than other schemes presented before based on current laboratory cavity-QED technology, and it is possible to be used as an applied unit gate in future quantum computation and quantum communication.
The phenomenological Maxwell field is quantized for arbitrarily space- and frequency-dependent complex permittivity. The formalism takes account of the Kramers--Kronig relation and the dissipation-fluctuation theorem and yields the fundamental equal-time commutation relations of QED. Applications to the quantum-state transformation at absorbing and amplifying four-port devices and to the spontaneous decay of an excited atom in the presence of absorbing dielectric bodies are discussed.
Whispering-gallery microcavity laser possesses ultralow threshold, whereas convenient free-space optical excitation and collection suffer from low efficiencies due to its rotational symmetry. Here we analytically study a three-dimensional microsphere coupled to a nano-sized scatterer in the framework of quantum optics. It is found that the scatterer is capable of coupling light in and out of the whispering-gallery modes (WGMs) without seriously degrading their high-Q properties, while the microsphere itself plays the role of a lens to focus the input beam on the scatterer and vice versa. Our a…
Recently a quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface (H.T. Dung, L. Knoell, and D.-G. Welsch, Phys. Rev. A 57, in press). Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commut…
We propose a way to realize a multiqubit tunable phase gate of one qubit simultaneously controlling n target qubits with atoms in cavity QED. In this proposal, classical pulses interact with atoms outside a cavity only, thus the experimental challenge of applying a pulse to an intra-cavity single atom without affecting other atoms in the same cavity is avoided. Because of employing a first-order large detuning, the gate can be performed fast when compared with the use of a second-order large detuning. Furthermore, the gate operation time is independent of the number of qubits. This proposal is…
The spontaneous emission rate of a radiating atom reaches its time-independent equilibrium value after an initial transient regime. In this paper we consider the associated relaxation effects of the spontaneous decay rate of atoms in dispersive and absorbing dielectric media for atomic transition frequencies near material resonances. A quantum mechanical description of such media is furnished by a damped-polariton model, in which absorption is taken into account through coupling to a bath. We show how all field and matter operators in this theory can be expressed in terms of the bath operators…
A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-v…
We extend Schwinger's ideas regarding sonoluminescence by explicitly calculating the Bogolubov coefficients relating the QED vacuum states associated with changes in a dielectric bubble. Sudden (non-adiabatic) changes in the refractive index lead to an efficient production of real photons with a broadband spectrum, and a high-frequency cutoff that arises from the asymptotic behaviour of the dielectric constant.
We propose a way to realize a multiqubit controlled phase gate with one qubit simultaneously controlling $n$ target qubits using atoms in cavity QED. In this proposal, there is no need of using classical pulses during the entire gate operation. The gate operation time scales as $\sqrt{n}$ only and thus the gate can be performed faster when compared with sending atoms through the cavity one at a time. In addition, only three steps of operations are required for realizing this $n$-target-qubit controlled phase gate. This proposal is quite general, which can be applied to other physical systems s…
Using carefully designed hybrid metal-dielectric resonators, we study molecular optomechanics in the strong coupling regime ($g_{\rm }^2/ω_m {>} κ$), which manifests in anharmonic emission lines in the sideband-resolved region of the cavity-emitted spectrum ($κ{<}ω_m$). This nonlinear optomechanical strong coupling regime is enabled through a metal-dielectric cavity system that yields not only deep sub-wavelength plasmonic confinement, but also dielectric-like confinement times that are more than two orders of magnitude larger than those from typical localized plasmon modes. These hybrid metal…
The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantu…
After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of dielectric matter of given space- and frequency-dependent complex permittivity can be transferred to quantum theory. Including in the theory the interaction of the medium-assisted field with atomic systems, we present both the minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in the Coulomb gauge. To illustrate the concept, we discuss the input--ou…
We have fabricated an atom chip device which combines the circuitry for magnetic trapping of cold atoms with high-finesse optical resonators suitable for cavity QED in the single-atom strong coupling regime. Fabry-Perot optical resonators with finesse F > 2 X 10^5 were formed between a micropatterned on-chip planar mirror with lateral dimension of < 100 um and a curved mirror suspended above the chip. The strong and rapid thermal coupling between on-chip electrical and optical elements was utilized to stabilize the cavity mirror separation with servo bandwidth exceeding 100 kHz during simulate…
We report on the loading of large ion Coulomb crystals into a linear Paul trap incorporating a high-Finesse optical cavity (F~3200). We show that, even though the 3-mm diameter dielectric cavity mirrors are placed between the trap electrodes and separated by only 12 mm, it is possible to produce in situ ion Coulomb crystals containing more than 100.000 calcium ions of various isotopes and with lengths of up to several millimeters along the cavity axis. We show that the number of ions inside the cavity mode is in principle high enough to achieve strong collective coupling between the ion Coulom…
We describe a tunable-cavity QED architecture with an rf SQUID phase qubit inductively coupled to a single-mode, resonant cavity with a tunable frequency that allows for both microwave readout of tunneling and dispersive measurements of the qubit. Dispersive measurement is well characterized by a three-level model, strongly dependent on qubit anharmonicity, qubit-cavity coupling and detuning. A tunable cavity frequency provides a way to strongly vary both the qubit-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the qubit, and residual bus co…
In a companion paper [quant-ph/9904013] we have investigated several variations of Schwinger's proposed mechanism for sonoluminescence. We demonstrated that any realistic version of Schwinger's mechanism must depend on extremely rapid (femtosecond) changes in refractive index, and discussed ways in which this might be physically plausible. To keep that discussion tractable, the technical computations in that paper were limited to the case of a homogeneous dielectric medium. In this paper we investigate the additional complications introduced by finite-volume effects. The basic physical scenari…
We present a scheme for deterministic ion-photon qubit exchange, namely a SWAP gate, based on realistic cavity-QED systems with 171Yb+, 40Ca+ and 138Ba+ ions. The gate can also serve as a single-photon quantum memory, in which an outgoing photon heralds the successful arrival of the incoming photonic qubit. Although strong coupling, namely having the single-photon Rabi frequency be the fastest rate in the system, is often assumed essential, this gate (similarly to the Duan-Kimble C-phase gate) requires only Purcell enhancement, i.e. high single-atom cooperativity. Accordingly, it does not requ…
There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling …
We consider a fibrillar medium with a continuous distribution of two-level atoms coupled to quantized electromagnetic fields. Perturbation theory is developed based on the current algebra satisfied by the atomic operators. The one-loop corrections to the dispersion relation for the polaritons and the dielectric constant are computed. Renormalization group equations are derived which demonstrate a screening of the two-level splitting at higher energies. Our results are compared with known results in the slowly varying envelope and rotating wave approximations. We also discuss the quantum sine-G…
We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multi-plasmon/photon Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission.…
An extensive characterization of high finesse optical cavities used in cavity QED experiments is described. Different techniques in the measurement of the loss and phase shifts associated with the mirror coatings are discussed and their agreement shown. Issues of cavity field mode structure supported by the dielectric coatings are related to our effort to achieve the strongest possible coupling between an atom and the cavity.
Contemporary experiments in cavity quantum electrodynamics (cavity QED) with gas-phase neutral atoms rely increasingly on laser cooling and optical, magneto-optical or magnetostatic trapping methods to provide atomic localization with sub-micron uncertainty. Difficult to achieve in free space, this goal is further frustrated by atom-surface interactions if the desired atomic placement approaches within several hundred nanometers of a solid surface, as can be the case in setups incorporating monolithic dielectric optical resonators such as microspheres, microtoroids, microdisks or photonic crys…
An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. Hybrid nanophotonic system with cold atoms has emerged as the paradigmatic platform for engineering long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at th…
The frequencies of transitions between hyperfine levels of ground-state atoms can be measured with exquisite precision using magnetic-resonance techniques. This makes hyperfine transitions ideal probes of QED effects originating from the interaction of atoms with the quantized electromagnetic field. One of the most remarkable effects predicted by QED is the Casimir-Polder shift experienced by the energy levels of atoms placed near one or more dielectric objects. Here we compute the Casimir-Polder shift and the width of hyperfine transitions between ground-state Zeeman sub-levels of an hydrogen…
In the standard theory of cavity quantum electrodynamics (QED), coupling between photons inside and outside a cavity (cavity system and photonic reservoir) is given conserving the total number of photons. However, when the cavity photons (ultra)strongly interact with atoms or excitations in matters, the system-reservoir coupling must be determined from a more fundamental viewpoint. Based on the Maxwell's boundary conditions in the QED theory for dielectric media, we derive the quantum Langevin equation and input-output relation, in which the total number of polaritons (not photons) inside the …
We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength, critical atom number N_0 and critical photon number n_0 for cesium are calculated…
We employ a recently developed quantization scheme for quasinormal modes (QNMs) to study a nonperturbative open cavity-QED system consisting of a hybrid metal-dielectric resonator coupled to a quantum emitter. This hybrid cavity system allows one to explore the complex coupling between a low $Q$ (quality factor) resonance and a high $Q$ resonance, manifesting in a striking Fano resonance, an effect that is not captured by traditional quantization schemes using normal modes or a Jaynes-Cummings (JC) type model. The QNM quantization approach rigorously includes dissipative coupling between the Q…
Instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at $Z>137/2$ for a spinless boson and at $Z>137$ for electron. Then, focus is concentrated on description of deep electron levels and spontaneous positron production in the field of a finite-size nucleus with the charge $Z>Z_{\rm cr}\simeq 170$. Next, these effects are studied in application to the low-energy heavy-ion collisions. Then, we consider phenomenon of "electron condensation" on levels of upper continuum crossed the boundary of the lower continuum $ε=-m$ in …
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of $N$, $M$, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the Matrix Product States technique. Both the time evolution for the field and qubits is computed. The nonlinear character (as a function of $N/M$) depends on the computed observable. While perfe…
We present and characterize fiber mirrors and a miniaturized ion-trap design developed to integrate a fiber-based Fabry-Perot cavity (FFPC) with a linear Paul trap for use in cavity-QED experiments with trapped ions. Our fiber-mirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trapped-ion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Op…
In this note we report on some new results \cite{SHP} on corrections to the Casimir-Polder \cite{caspol} retardation force due to atomic motion and present a preliminary (unpublished) critique on one recently proposed cavity QED detection scheme of Unruh effect \cite{Unr76}. These two well-known effects arise from the interaction between a moving atom or detector with a quantum field under some boundary conditions introduced by a conducting mirror/cavity or dielectric wall. The Casimir-Polder force is a retardation force on the atom due to the dressing of the atomic ground state by the vacuum …
Cavity Control of Strongly Correlated Electrons Beyond Resonant Coupling
RWTH Aachen University（亚琛工业大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马普研究所）；Max Planck Institute for the Physics of Complex Systems（复杂系统物理马普研究所）
