Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the $s$-parameterized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.
The interaction between quantum light and matter is being intensively studied for systems that are enclosed in high-$Q$ cavities which strongly enhance the light-matter coupling. However, for many applications, cavities with lower $Q$-factors are preferred due to the increased spectral width of the cavity mode. Here, we investigate the interaction between quantum light and matter represented by a $Λ$-type three-level system in lossy cavities, assuming that cavity losses are the dominant loss mechanism. We demonstrate that cavity losses lead to non-trivial steady states of the electronic occupa…
Here we consider the continuous pumping of a dissipative QED cavity and derive the time-dependent density operator of the cavity field prepared initially as a superposition of mesoscopic coherent states. The control of the coherence of this superposition is analyzed considering the injection of a beam of two-level Rydberg atoms through the cavity. Our treatment is compared to other approaches.
We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the C…
A recent work [1] proposed a type of cluster entangled coherent states and its generation. Here we present an alternative experimental arrangement for its generation in bimodal QED cavities. The scheme employs a single two-level atom that interacts dispersively with cavity modes initially prepared in coherent states. The fidelity and success probability of the state preparation are obtained considering the influence of atomic velocity spread and atomic efficiency detection.
We propose an experiment with two coupled microwave cavities and a "tunneling" photon observed by the passage of Rydberg atoms. We model the coupled cavities as in Ref. \cite{art1} and include dissipative effects as well as limited detection efficiency. We also consider realistic finite atom-field interaction times and provide for a simple analytical expression for the photon "tunneling" probability including all these effects. We show that for sufficiently small dissipation constants the effect can be observed with current experimental facilities.
We investigate theoretically the properties of squeezed states generated using degenerate parametric down conversion in lossy cavities. We show that the Lindblad master equation, which governs the evolution of this system, has as its solution a squeezed thermal state with an effective temperature and squeezing parameter that depends on time. We derive analytical solutions for the time-evolution of quadrature noise, thermal photon number, squeezing parameter, and total photon number under different pumping regimes. We also find the steady state limits of the quadrature noises and discuss the $ …
We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate…
Position-Resolved Resonance Quantization for Lossy Cavities
Albert-Ludwigs-Universität Freiburg（弗赖堡大学）；EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg（阿尔伯特-路德维希-弗赖堡大学 EUCOR 量子科学与量子计算中心）
We present evidence of cavity quantum electrodynamics from a sparse density of strongly quantum-confined Pb-chalcogenide nanocrystals (between 1 and 10) approaching single-dot levels on moderately high-Q mesoscopic silicon optical cavities. Operating at important near-infrared (1500-nm) wavelengths, large enhancements are observed from devices and strong modifications of the QD emission are achieved. Saturation spectroscopy of coupled QDs is observed at 77K, highlighting the modified nanocrystal dynamics for quantum information processing.
In this article we discuss two schemes of teleportation of cavity field states. In the first scheme we consider cavities prepared in a coherent state and in the second scheme we consider cavities prepared in a superposition of zero and one Fock states.
By exploiting a system of three distant cavities, we propose a scheme for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entan-gled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negli-gible the destruction of entanglement due to decoherence arises from photon losses, is effective…
Research on photonic cavities with low mode volume and high quality factor garners much attention because of applications ranging from optoelectronics to cavity quantum electrodynamics (QED). We propose a cavity based on surface plasmon modes confined by metallic distributed Bragg reflectors. We analyze the structure with Finite Difference Time Domain simulations and obtain modes with quality factor 1000 (including losses from metals), reduced mode volume relative to photonic crystal cavities, Purcell enhancements of hundreds, and even the capability of enabling cavity QED strong coupling.
We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity QED parameters and with nonideal coupling.
The paper continues the analysis of vacuum Rabi oscillations we started in Part I [Phys. Rev. A {\bf 79}, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic oscillator Lie algebras. The zero-temperature master equation, derived in Part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic fields by a gas of harmonic oscillator wave packets. The representation is known to introduce automatic regularizations that in irreducible representations…
We propose a scheme on the basis of a N+2 identical single-mode coupled-cavity QED system for selective transfer of a qubit constructed from superposition of standard coherent states. The cavities arranged in such way that the intermediate or channel cavity is connected uniformly to the sender and N receiver cavities. We consider N different ternary sets of identical QDs whose QDs have been distributed in the sender, channel and one of the receiver cavities respectively. We demonstrate a situation in which the dynamics of the system is confined selectively in a sub sector belongs to one of the…
We propose a scheme for quantum computing using high-Q cavities in which the qubits are represented by single cavity modes restricted in the space spanned by the two lowest Fock states. We show that single qubit operations and universal multiple qubit gates can be implemented using atoms sequentially crossing the cavities.
In a cavity quantum electrodynamics (QED) system, where atoms coherently interact with photons in a cavity, the eigenstates of the system are the superposition states of atoms and cavity photons, the so-called dressed states of atoms. When two cavities are connected by an optical fiber with negligible loss, the coherent coupling between the cavities gives rise to photonic normal modes. One of these normal modes is the fiber-dark mode, in which photons are delocalized in the two distant cavities. Here we demonstrate the setting of coupled-cavities QED, where two nanofiber cavity-QED systems are…
A potential scheme is proposed to generate complete sets of entangled photons in the context of cavity quantum electrodynamics (QED). The scheme includes twice interactions of atoms with cavities, in which the first interaction is made in two-mode optical cavities and the second one exists in a microwave cavity. In the optical cavities the atoms are resonant with the cavity modes, while the detuned interaction of the atoms with a single-mode of the microwave cavity is driven by a classical field. We show that our scheme is carried out with higher efficiency than previeous schemes, and is close…
We propose a method for transferring quantum entangled states of two photonic cat-state qubits (cqubits) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resources is minimized. The entanglement transfer is completed with a single-step operation only, thus this proposal is quite simple. The third energy level of the co…
The 1996 Brune {\it et al.} experiment on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis, and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is $Q=3.31\cdot 10^{10}$, whereas…
We investigate the phenomenon of sudden transition between classical and quantum decoherence in the study of quantum discord for a dissipative cavity QED system, which consists of two noninteracting two-level atoms, each trapped in a dissipative cavity. It is found that the quantum discord between two atoms, which are prepared initially in the X-type quantum states, is not destroyed by the dissipation of the cavities for a finite time interval and the stationary quantum discord can arise in the interaction of atoms with cavities as the time approach to infinite. The transition time is sensitiv…
We analyze a coupling scheme for qubits in different cavities of circuit-QED architecture. In contrast to the usual scheme where the cavities are coupled by an interface capacitance we employ a bridge qubit connecting cavities to mediate two-qubit coupling. This active coupling scheme makes it possible to switch on/off and adjust the strength of qubit-qubit coupling, which is essential for scalability of quantum circuit. By transforming the Hamiltonian we obtain an exact expression of two-qubit coupling in the rotating-wave approximation. For the general case of $n$ qubits the Hamiltonian can …
We introduce a scheme for perfect routing of quantum states and entanglement in regular cavity QED networks. The couplings between the cavities are quasi-uniform and each cavity is doped with a two-level atom. Quasi-uniform couplings leads the system to evolve in invariant subspaces. Combination the evolutions of the system in its invariant subspaces with quite simple local operations on atoms in the networks, gives the perfect routing of quantum states and entanglement through the network. To provide the protocol be robust due to decoherence arisen from photon loss, the field mode of the cavi…
We study the zero-temperature phase diagram of a one-dimensional array of QED cavities where, besides the single-photon hopping, an additional coupling between neighboring cavities is mediated by an N-type four-level system. By varying the relative strength of the various couplings, the array is shown to exhibit a variety of quantum phases including a polaritonic Mott insulator, a density-wave and a superfluid phase. Our results have been obtained by means of numerical density-matrix renormalization group calculations. The phase diagram was obtained by analyzing the energy gaps for the polarit…
We show that coherent control of the steady-state long-distance entanglement between pairs of cavity-atom systems in an array of lossy and driven coupled resonators is possible. The cavities are doped with atoms and are connected through wave guides, other cavities or fibers depending on the implementation. We find that the steady-state entanglement can be coherently controlled through the tuning of the phase difference between the driving fields. It can also be surprisingly high in spite of the pumps being classical fields. For some implementations where the connecting element can be a fiber,…
We report a process for fabricating high quality, defect-free spherical mirror templates suitable for developing high finesse optical Fabry-Perot resonators. The process utilizes the controlled reflow of borosilicate glass and differential pressure to produce mirrors with 0.3 nanometer surface roughness. The dimensions of the mirrors are in the 0.5-5mm range making them suitable candidates for integration with on-chip neutral atom and ion experiments where enhanced interaction between atoms and photons are required. Moreover the mirror curvature, dimension and placement is readily controlled a…
Plasmon-enhanced Raman scattering can push single-molecule vibrational spectroscopy beyond a regime addressable by classical electrodynamics. We employ a quantum electrodynamics (QED) description of the coherent interaction of plasmons and molecular vibrations that reveal the emergence of nonlinearities in the inelastic response of the system. For realistic situations, we predict the onset of \textit{phonon-stimulated Raman scattering} and an counter-intuitive dependence of the anti-Stokes emission on the frequency of excitation. We further show that this novel QED framework opens a venue to a…
Suggestion of modifications of finite-dimensional QED models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage…
We propose and analyze a physical implementation of two-qubit parity measurements as required for continuous error correction, assuming a setup in which the individual qubits are strongly coupled to separate optical cavities. A single optical probe beam scatters sequentially from the two cavities and the continuous parity measurement is realized via fixed quadrature homodyne photo-detection. We present models based on quantum stochastic differential equations (QSDE's) for both an ideal continuous parity measurement and our proposed cavity quantum electrodynamics (cavity QED) implementation; a …
In this article we discuss a teleportation scheme of coherent states of cavity field. The experimental realization proposed makes use of cavity quatum electrodynamics involving the interaction of Rydberg atoms with micromaser and Ramsey cavities. In our scheme the Ramsey cavities and the atoms play the role of auxiliary systems used to teleport the state from a micromaser cavity to another. We show that, even if the correct atomic detection fails in the first trials, one can succeed in teleportating the cavity field state if the proper measurement occurs in a later atom.
We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight binding approximation and apply this to a two-cavity system as well as to a coupled resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time dependant cross correlation between the photons in different cavities to …
In the framework of cavity QED, we propose a quantum repeater scheme that uses coherent light and atoms coupled to optical cavities. In contrast to conventional schemes, we exploit solely the cavity QED evolution for the entire quantum repeater scheme and, thus, avoid any explicit execution of quantum logical gates. The entanglement distribution between the repeater nodes is realized with the help of pulses of coherent light interacting with the atom-cavity system in each repeater node. In our previous paper [D. Gonta and P. van Loock, Phys. Rev. A 86, 052312 (2012)], we already proposed a dyn…
We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An exper…
We propose to detect the Mott insulator-superfluid quantum phase transition in an array of coupled cavities by studying the polariton and photon fluctuations in a block of linear dimension M (in units of the lattice constant of the array). We explicitly show this for a one-dimensional array; the analysis can be however extended to higher dimensions. In the Mott phase polariton fluctuations are independent of the block size. In the superfluid phase they grow logarithmically with M, the prefactor being related to the compressibility of the system. In the case of photon fluctuations, the critical…
We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting quantum dynamics in general. The user is provided with a number of ``elements'', eg pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulatio…
We investigate chiral emission and the single-photon scattering of spinning cavities coupled to a meandering waveguide at multiple coupling points. It is shown that nonreciprocal photon transmissions occur in the cavities-waveguide system, which stems from interference effects among different coupling points, and frequency shifts induced by the Sagnac effect. The nonlocal interference is akin to the mechanism in giant atoms. In the single-cavity setup, by optimizing the spinning velocity and number of coupling points, the chiral factor can approach 1, and the chiral direction can be freely swi…
In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter-photon problems. Therefore, we analyze model systems in optical cavities, where the matter-photon interaction is considered from the weak- to the strong coupling limit and for individual photon modes as well as for the multi-mode case. We identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic quantities, conical intersections and efficiency for quantum control. …
We study the propagation and distribution of quantum correlations through two chains of atoms inside cavities joined by optical fibers. We consider an effective Hamiltonian for the system and cavity losses, in the dressed atom picture, using the Generalized Master Equation.
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.…
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the t…
Based on a multimode multilevel Jaynes-Cummings model and multiphoton resonance theory, a set of universal two- and three-qubit gates, namely the iSWAP and the Fredkin gates, has been realized where dual-rail qubits are encoded in cavities. In this way the information has been stored in cavities and the off-resonant atomic levels have been eliminated by the semi-classical theory of an effective two-level Hamiltonian. A further semi-classical model, namely the spin-$J$ model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multil…
We calculate the weak-driving transmission of a linearly polarized cavity mode strongly coupled to the D2 transition of a single Cesium atom. Results are relevant to future experiments with microtoroid cavities, where the single-photon Rabi frequency g exceeds the excited-state hyperfine splittings, and photonic bandgap resonators, where g is greater than both the excited- and ground-state splitting.
Multimode cavity quantum electrodynamics ---where a two-level system interacts simultaneously with many cavity modes---provides a versatile framework for quantum information processing and quantum optics. Due to the combination of long coherence times and large interaction strengths, one of the leading experimental platforms for cavity QED involves coupling a superconducting circuit to a 3D microwave cavity. In this work, we realize a 3D multimode circuit QED system with single photon lifetimes of $2$ ms and cooperativities of $0.5-1.5\times10^9$ across 9 modes of a novel seamless cavity. We d…
In the framework of cavity QED, we propose a practical scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid CNOT gates, thus reducing complicated pulse sequences and superfluous qubit operations. Our interaction scheme works in a deterministic way, and together with entanglement distribution and swapping, opens a route towards efficient quantum repeaters for long-distance quantum communication.
In distributed quantum information processing, flying photons entangle matter qubits confined in cavities. However, when a matter qubit is homogeneously broadened, the strong-coupling regime of cavity QED is typically required, which is hard to realize in actual experimental setups. Here, we show that a high-fidelity entanglement operation is possible even in the weak-coupling regime in which dampings (dephasing, spontaneous emission, and cavity leakage) overwhelm the coherent coupling between a qubit and the cavity. Our proposal enables distributed quantum information processing to be perform…
We propose a cavity-QED scheme that can deterministically generate Einstein-Podosky-Rosen polarization-entangled photon pairs. A four-level tripod atom successively couples to two high-Q optical cavities possessing polarization degeneracy, assisted by a classical $π$-polarized pump field. The stimulated Raman adiabatic passage process in the atom-cavity system is used to produce the polarization-entangled photon pairs. The proposal is particularly robust against atomic spontaneous decay, which should have potential applications in quantum information processing.
We propose a new scheme of measurement-based quantum computation (MBQC) using an error-correcting code against photon-loss in circuit quantum electrodynamics. We describe a specific protocol of logical single-qubit gates given by sequential cavity measurements for logical MBQC and a generalised Schrödinger cat state is used for a continuous-variable (CV) logical qubit captured in a microwave cavity. It is assumed that a three CV-qudit entangled state is initially prepared in three jointed cavities and the microwave qudit states are individually controlled, operated, and measured through a read…
We explore the photon population dynamics in two coupled circuit QED systems. For a sufficiently weak inter-cavity photon hopping, as the photon-cavity coupling increases, the dynamics undergoes double transitions first from a delocalized to a localized phase and then from the localized to another delocalized phase. The latter delocalized phase is distinguished from the former one; instead of oscillating between the two cavities, the photons rapidly quasi-equilibrate over the two cavities. These intrigues are attributed to an interplay between two qualitatively distinctive nonlinear behaviors …
We propose an oversimplified scheme to unambiguously discriminate nonorthogonal quantum field states inside high-Q cavities. Our scheme, which is based on positive operator-valued mea- sures (POVM) technique, uses a single three-level atom interacting resonantly with a single mode of a cavity-field and selective atomic state detectors. While the single three-level atom takes the role of the ancilla, the single cavity mode field represents the system we want to obtain information. The efficiency of our proposal is analyzed considering the nowadays achievements in the context of cavity QED.
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…
The dynamics of a vibronic system in a lossy two-mode cavity is studied, with the first mode being resonant to the electronic transition and the second one being nearly resonant due to Raman transitions. We derive analytical solutions for the dynamics of this system. For a properly chosen detuning of the second mode from the exact Raman resonance, we obtain conditions that are closely related to the phenomenon of Rabi resonance as it is well known in laser physics. Such resonances can be observed in the spontaneous emission spectra, where the spectrum of the second mode in the case of weak Ram…
We present a probabilistic scheme for generating and purifying maximally-entangled states of two atoms inside an optical cavity via no-photon detection in the output cavity mode, where ideal detectors may not be required. The intermediate mixed states can be continuously "filtered" so as to violate Bell inequalities in a parametrized manner. The scheme relies on an additional strong-driving field that yields unusual dynamics in cavity QED experiments, simultaneously realizing Jaynes-Cummings and anti-Jaynes-Cummings interactions.
The ability to accumulate and retrieve entanglement in the fields of two remote cavities with pairs of two-level atoms is discussed. It is shown that this transfer and retrieval can be indeed ideal with a resonant interaction. The case of initial non-maximally entangled atomic pairs is also considered. This leads to the possibility of concentrating entanglement into a single pair at the retrieval stage. A teleportation protocol based on the same setup is presented. This makes possible teleportation with built-in entanglement concentration.
Photonic band gap (PBG) materials are attractive for cavity QED experiments because they provide extremely small mode volumes and are monolithic, integratable structures. As such, PBG cavities are a promising alternative to Fabry-Perot resonators. However, the cavity requirements imposed by QED experiments, such as the need for high Q (low cavity damping) and small mode volumes, present significant design challenges for photonic band gap materials. Here, we pose the PBG design problem as a mathematical inversion and provide an analytical solution for a two-dimensional crystal. We then address …
Both cavity QED and photons are promising candidates for quantum information processing. We consider a combination of both candidates with a single photon going through spatially separate cavities to entangle the atomic qubits, based on the input-output process of the cavities. We present a general expression for the input-output process regarding the low-Q cavity confining a single atom, which works in a wide range of parameters. Focusing on low-Q cavity case, we propose some schemes for quantum information processing with Faraday rotation using single photons, which is much different from th…
