We introduce the quantum quincunx, which physically demonstrates the quantum walk and is analogous to Galton's quincunx for demonstrating the random walk. In contradistinction to the theoretical studies of quantum walks over orthogonal lattice states, we introduce quantum walks over nonorthogonal lattice states (specifically, coherent states on a circle) to demonstrate that the key features of a quantum walk are observable albeit for strict parameter ranges. A quantum quincunx may be realized with current cavity quantum electrodynamics capabilities, and precise control over decoherence in such experiments allows a remarkable decrease in the position noise, or spread, with increasing decoherence.
We show how a quantum walk can be implemented for the first time in a quantum quincunx created via superconducting circuit quantum electrodynamics (QED), and how interpolation from quantum to random walk is implemented by controllable decoherence using a two resonator system. Direct control over the coin qubit is difficult to achieve in either cavity or circuit QED, but we show that a Hadamard coin flip can be effected via direct driving of the cavity, with the result that the walker jumps between circles in phase space but still exhibits quantum walk behavior over 15 steps.
We show how multi-walker quantum walks can be implemented in a quantum quincunx created via cavity quantum electrodynamics. The implementation of a quantum walk with a multi-walker opens up the interesting possibility to introduce entanglement and more advanced walks. With different coin tosses and initial states the multi-walker quantum walk shows different probability distributions which deviate strongly from the classical random walks with quadratic enhanced spreadings and localization effects. By introducing decoherence, the transition from quantum walks to the classical versions is observ…
In this article we discuss a scheme of teleportation of atomic states. The experimental realization proposed makes use of cavity Quatum Electrodynamics involving the interaction of Rydberg atoms with a micromaser cavity prepared in a coherent state. We start presenting a scheme to prepare atomic Bell states via the interaction of atoms with a cavity. In our scheme the cavity and some atoms play the role of auxiliary systems used to achieve the teleportation.
We propose an experimentally feasible scheme to realize the nonlocal gate between two different quantum network nodes. With an entanglement-qubit (ebit) acts as a quantum channel, our scheme is resistive to actual environment noise and can get high fidelity in current cavity quantum electrodynamics (C-QED) system.
We study universal quantum computation in the cavity quantum electrodynamics (CQED) framework exploiting two orthonormal two-photon generalized binomial states as qubit and dispersive interactions of Rydberg atoms with high-$Q$ cavities. We show that an arbitrary qubit state may be generated and that controlled-NOT and 1-qubit rotation gates can be realized via standard atom-cavity interactions.
In this letter we present a scheme for the implementation of frequency up- and down-conversion operations in two-mode cavity quantum electrodynamics (QED). This protocol for engineering bilinear two-mode interactions could enlarge perspectives for quantum information manipulation and also be employed for fundamental tests of quantum theory in cavity QED. As an application we show how to generate a two-mode squeezed state in cavity QED (the original entangled state of Einstein-Podolsky-Rosen).
In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics (QED) through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.
We describe the absorption by the walls of a quantum electrodynamics cavity as a process during which the elementary excitations (photons) of an internal mode of the cavity exit by tunneling through the cavity walls. We estimate by classical methods the survival time of a photon inside the cavity and the quality factor of its mirrors.
We propose a method to perform single-shot optical readout of a quantum bit (qubit) using cavity quantum electrodynamics. We selectively couple the optical transitions associated with different qubit basis states to the cavity, and utilize the change in cavity transmissivity to generate a qubit readout signal composed of many photons. We show that this approach enables single-shot optical readout even when the qubit does not have a good cycling transition required for standard resonance fluorescence measurements. We calculate the probability that the measurement detects the correct spin state …
Cavity quantum electrodynamic schemes for quantum gates are amongst the earliest quantum computing proposals. Despite continued progress, and the dramatic recent demonstration of photon blockade, there are still issues with optimal coupling and gate operation involving high-quality cavities. Here we show dynamic control techniques that allow scalable cavity-QED based quantum gates, that use the full bandwidth of the cavities. When applied to quantum gates, these techniques allow an order of magnitude increase in operating speed, and two orders of magnitude reduction in cavity Q, over passive c…
When ground state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The cavity field at steady state is described by a thermal density matrix under most conditions. However, under some conditions gain is possible, and when the atoms are injected in a regular fashion, the radiation can be produced in a squeezed state.
We show that photon coincidence spectroscopy can provide an unambiguous signature of two atoms simultaneously interacting with a quantised cavity field mode. We also show that the single-atom Jaynes-Cummings model can be probed effectively via photon coincidence spectroscopy, even with deleterious contributions to the signal from two-atom events. In addition, we have explicitly solved the eigenvectors and eigenvalues of two two-level atoms coupled to a quantised cavity mode for differing coupling strengths.
Using a single circular Rydberg atom, we have prepared two modes of a superconducting cavity in a maximally entangled state. The two modes share a single photon. This entanglement is revealed by a second atom probing, after a delay, the correlations between the two modes. This experiment opens interesting perspectives for quantum information manipulation and fundamental tests of quantum theory.
A large payload quantum steganography protocol based on cavity quantum electrodynamics (QED) is presented in the paper, which effectively uses the evolution law of atom in cavity QED. The protocol builds up hidden channel to transmit secret messages using entanglement swapping between one GHZ state and one Bell state in cavity QED together with the Hadamard operation. The quantum steganography protocol is insensitive to cavity decay and thermal field. The capacity, imperceptibility and security against eavesdropping are analyzed in detail in the protocol. It turns out that the protocol not onl…
We construct a model which describes a recently performed experiment (Phys. Rev. A 64, 050301(R) (2001)) in which an entangled state between two modes of a single cavity is built. Environmental effects are taken into account and the results agree with the experimental findings. Moreover the model predicts, for different conditions of the same experiment, a decoherence-free subspace. These conditions are analyzed and slightly different experiments suggested in order to test its viability.
We present a general framework for cavity quantum electrodynamics with strongly frequency-dependent mirrors. The method is applicable to a variety of reflectors exhibiting sharp internal resonances as can be realized, for example, with photonic-crystal mirrors or with two-dimensional atomic arrays around subradiant points. Our approach is based on a modification of the standard input--output formalism to explicitly include the dynamics of the mirror's internal resonance. We show how to directly extract the interaction tuning parameters from the comparison with classical transfer matrix theory …
We present coherent reflection spectroscopy on a charge and DC Stark tunable quantum dot embedded in a high-quality and externally mode-matched microcavity. The addition of an exciton to a single-electron charged quantum dot forms a trion that interacts with the microcavity just below strong coupling regime of cavity quantum electrodynamics. Such an integrated, monolithic system is a crucial step towards the implementation of scalable hybrid quantum information schemes that are based on an efficient interaction between a single photon and a confined electron spin.
In this paper we investigate the various aspects of noise and order in the micromaser system. In particular, we study the effect of adding fluctuations to the atom cavity transit time or to the atom-photon frequency detuning. By including such noise-producing mechanisms we study the probability and the joint probability for excited atoms to leave the cavity. The influence of such fluctuations on the phase structure of the micromaser as well as on the long-time atom correlation length is also discussed. We also derive the asymptotic form of micromaser observables.
We introduce a new scalable cavity quantum electrodynamics platform which can be used for quantum computing. This system is composed of coupled photonic crystal (PC) cavities which their modes lie on a Dirac cone in the whole super crystal band structure. Quantum information is stored in quantum dots that are positioned inside the cavities. We show if there is just one quantum dot in the system, energy as photon is exchanged between the quantum dot and the Dirac modes sinusoidally. Meanwhile the quantum dot becomes entangled with Dirac modes. If we insert more quantum dots into the system, the…
We analytically derive the upper bound on the overall efficiency of single-photon generation based on cavity quantum electrodynamics (QED), where cavity internal loss is treated explicitly. The internal loss leads to a tradeoff relation between the internal generation efficiency and the escape efficiency, which results in a fundamental limit on the overall efficiency. The corresponding lower bound on the failure probability is expressed only with an "internal cooperativity," introduced here as the cooperativity parameter with respect to the cavity internal loss rate. The lower bound is obtaine…
We propose a Markovian quantum master equation that can describe the Fano effect directly, by assuming a standard cavity quantum electrodynamics system. The framework allows us to generalize the Fano formula, applicable over the weak and strong coupling regimes with pure dephasing. A formulation of its emission spectrum is also given in a consistent manner. We then find that the interference responsible for the Fano effect is robust against pure dephasing. This is counterintuitive because the impact of interference is, in general, severely reduced by decoherence processes. Our approach thus pr…
We investigate theoretically the model of a cavity-quantum-electrodynamics (QED) system that consists of two two-level atoms coupled to a single-mode cavity in the weak coupling regime, where the system is driven by quantum light. The dynamics behavior of the entire system is tackled in the framework of a cascaded quantum system. We find that the two-photon blockade with two-photon bunching and three-photon antibunching can be obtained even when the strong system dissipation is included. This result shows that our work has potential for realizing entangled photon pairs in a weakly coupled cavi…
We theoretically study the properties of highly prolate shaped dielectric microresonators. Such resonators sustain whispering gallery modes that exhibit two spatially well separated regions with enhanced field strength. The field per photon on the resonator surface is significantly higher than e.g. for equatorial whispering gallery modes in microsphere resonators with a comparable mode volume. At the same time, the frequency spacing of these modes is much more favorable, so that a tuning range of several free spectral ranges should be attainable. We discuss the possible application of such res…
We describe an electrodynamic mechanism for coherent, quantum mechanical coupling between spacially separated quantum dots on a microchip. The technique is based on capacitive interactions between the electron charge and a superconducting transmission line resonator, and is closely related to atomic cavity quantum electrodynamics. We investigate several potential applications of this technique which have varying degrees of complexity. In particular, we demonstrate that this mechanism allows design and investigation of an on-chip double-dot microscopic maser. Moreover, the interaction may be ex…
Utilizing the continuous frequency mode quantization scheme, we study from first principle the efficiency of a feedback scheme that can generate maximally entangled states of two atoms in an optical cavity through their interactions with a single input photon. The spectral function of the photon emitted from the cavity, which will be used as the input of the next round in the feedback process, is obtained analytically. We find that the spectral function of the photon is modified in each round and deviates from the original one. The efficiency of the feedback scheme consequently deteriorates gr…
Cavity quantum electrodynamics (CQED) investigates the interaction between light confined in a resonator and particles, such as atoms. In recent years, CQED experiments have reached the optical domain resulting in many interesting applications in the realm of quantum information processing. For many of these application it is necessary to overcome limitations imposed by photon loss. In this context whispering-gallery mode (WGM) resonators have obtained significant interest. Besides their small mode volume and their ultra high quality, they also exhibit favorable polarization properties that gi…
We revisit the mathematical formulation of the famous Jaynes-Cummings-Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the condition of Ultrastrong coupling between the atom and cavity, in which the transition frequency is comparable to the coupling frequency, the bosonic field operators undergo non-sinusoidal time variations. As a result, the well-known solutions to the Jaynes-Cummings-Paul model are no longer valid, even when the rotating wave approximation is not used. We show how a…
In this paper, we present a protocol to engineer upper-bounded and sliced Jaynes-Cummings and anti-Jaynes-Cummings Hamiltonians in cavity quantum electrodynamics. In the upper-bounded Hamiltonians, the atom-field interaction is confined to a subspace of Fock states ranging from $\left\vert 0\right\rangle $ up to $\left\vert 4\right\rangle $, while in the sliced interaction the Fock subspace ranges from $\left\vert M\right\rangle $ up to $\left\vert M+4\right\rangle $. We also show how to build upper-bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper-bounded and…
Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which an atomic ensemble interacts coherently with a single resonant cavity mode. The interacting system can be effectively described by two coupled oscillators with positive and negative mass when the two-level atoms are prepared in their excited states. The occurrence of symmetry breaking is controlled by the atomic detuning and the coupling to the cavity mode, …
We investigate the cavity excitation spectrum and the photon number distribution in a cavity QED system driven by a broadband squeezed vacuum. In an empty cavity, we show that only states with even number of photons can be measured under resonant condition since the squeezed vacuum consists of states with even number of photons only. When a single atom is trapped in the cavity, the strong coupling between the atom and cavity results in energy splittings of the system, and there exist two peaks in the cavity excitation spectrum at two-photon transition frequencies. At the central frequency, how…
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 study the transmission spectra of ultracold rubidium atoms coupled to a high-finesse optical cavity. Under weak probing with pi-polarized light, the linear response of the system is that of a collective spin with multiple levels coupled to a single mode of the cavity. By varying the atom number, we change the collective coupling of the system. We observe the change in transmission spectra when going from a regime where the collective coupling is much smaller than the separation of the atomic levels to a regime where both are of comparable size. The observations are in good agreement with a …
We investigate spontaneous photon emission and absorption processes of two two-level atoms trapped close to the focal points of an ellipsoidal cavity, thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms by describing the field modes semiclassically. Based on this approach, we express the excitation probabilities by a semiclassical photon path representation. Due to the special property of an ellipsoidal cavity of having two focal points, we are able to study interesting intermediate instances between well-known quantum-…
The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors/amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED…
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and swapping-based operations that together provide implementation of any encoded single-qubit operation by three elementary gates and the encoded controlled-NOT operation is performed in a single step. This approach simplifies a physical realization of universal quantum computing and adds the immunity to a number of errors. We also demonstrate that the proposed a…
A quantum computer is proposed in which information is stored in the two lowest electronic states of doped quantum dots (QDs). Many QDs are located in a microcavity. A pair of gates controls the energy levels in each QD. A Controlled Not (CNOT) operation involving any pair of QDs can be effected by a sequence of gate-voltage pulses which tune the QD energy levels into resonance with frequencies of the cavity or a laser. The duration of a CNOT operation is estimated to be much shorter than the time for an electron to decohere by emitting an acoustic phonon.
We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehrenfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the ca…
Strongly driven cavity quantum electrodynamical-optomechanical hybrid system
Laboratory of Photonics and Quantum Measurements (LPQM), Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院光子与量子测量实验室）；Center for Quantum Science and Engineering, EPFL（洛桑联邦理工学院量子科学与工程中心）
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 present a novel representation of coupled matter-photon systems that allows the application of many-body methods developed for purely fermionic systems. We do so by rewriting the original coupled light-matter problem in a higher-dimensional configuration space and then use photon-dressed orbitals as a basis to expand the thus "fermionized" coupled system. As an application we present a dressed time-dependent density-functional theory approach. The resulting dressed Kohn-Sham scheme allows for straightforward non-adiabatic approximations to the unknown exchange-correlation potential that exp…
We studied the interaction of a two-level atom with a frequency modulated cavity mode in an ideal optical cavity. The system, described by a Jaynes-Cumming Hamiltonian, gave rise to a set of stiff nonlinear first order equations solved numerically using implicit and semi-implicit numerical algorithms. We explored the evolution of the atomic system using nonlinear dynamics tools, like time series, phase plane, power spectral density, and Poincaré sections plots, for monochromatic and bichromatic modulations of the cavity field. The system showed quasiperiodic and possibly chaotic behavior when …
Here, a comprehensive theory of the couplings between a nanocavity and exciton complexes in a quantum dot is developed, which successfully predicts the spectral triplet in the strong coupling regime that has been observed in several experiments but is unexpected according to conventional cavity quantum electrodynamics. The quantum anti-Zeno effect is found to play an essential role in the appearance of the central peak in the triplet under a low-excitation regime. The effect of hyperfine interactions is also discussed, which results in the cavity-mediated mixing of bright and dark exciton stat…
Controlling the time evolution of the population of two states in cavity quantum electrodynamics (QED) is necessary by tunning the \textit{modified} Rabi frequency in which the $\textit{extra}$ classical effect of electromagnetic field is taken into account.The theoretical explanation underlying the perturbation of potential on spatial regime of bloch sphere is by the use of (Bagrov, Baldiotti, Gitman, and Shamshutdinova) BBGS-Darboux transformations \cite{bagrov14darboux} on the electromagnetic field potential in one-dimensional stationary Dirac model in which the Pauli matrices are the centr…
Spontaneously generated coherence and enhanced dispersion in a V-type, three-level atomic system interacting with a single mode field can considerably reduce the radiative and cavity decay rates. This may eliminate the use of high finesse, miniaturized cavities in optical cavity quantum electrodynamics experiments under strong atom-field coupling conditions.
The possibility of a superradiant phase transition in light-matter systems is the subject of much debate, due to numerous apparently conflicting no-go and counter no-go theorems. Using an arbitrary gauge approach we show that a unique phase transition does occur in archetypal many-dipole cavity QED systems, and that it manifests unambiguously via a macroscopic gauge-invariant polarisation. We find that the gauge choice controls the extent to which this polarisation is included as part of the radiative quantum subsystem and thereby determines the degree to which the abnormal phase is classed as…
The insertion of a small polarizable particle in an arbitrarily large optical cavity significantly alters the quantum-mechanical state of the electromagnetic field in that the photon ground state of the empty cavity and that of the cavity with the particle become mutually orthogonal and, thus, cannot be connected adiabatically in the infinite limit. The photon problem can be mapped exactly onto that of a many-body system of fermions, which is known to exhibit an orthogonality catastrophe when a finite-range local potential is introduced. We predict that the motion of polarizable objects inside…
Since the photon box gedanken experiments of several of the founding fathers of modern physics, considerable progress has been made in differentiating the quantum and classical worlds. In this pursuit, the cavity as an open quantum system has been indispensable. From the quantization of the atom and field within a superconducting cavity, a unique realm of EPR type entanglement has emerged. In this way, dynamical evolution of the system in the strong coupling regime is intimately tied with the coupling of an atom with a single resonant or non-resonant mode within the cavity. More specifically, …
Vacuum induced coherence in a strongly coupled cavity consisting of a three-level system is studied theoretically. The effects of the strong coupling to electromagnetic field vacuum are examined by solution of an open-system quantum master equation. The numerical results show that the system exhibits population trapping, and the numerical results are interpreted with analytical expressions derived from a new basis in the weak excitation regime. We further show that the generated effects can be probed with weak external fields. Moreover, it is shown that the induced coherence can be controlled …
A dressed-state perturbation theory beyond the rotating waveapproxi-mation (RWA) is presented to investigate the interaction between a two level electronic transition of the polar molecules and a quantized cavity field. Analytical expressions can be explicitly derived for both the ground- and excited-state-energy spectrums and wave functions of the system, where the contribution of permanent dipole moments (PDM) and the counter-rotating wave term (CRT) can be shown separately. The validity of these explicit results is discussed by comparing with the direct numerical simulation. Comparing to CR…
Tripartite Entanglement in Multimode Cavity Quantum Electrodynamics
Department of Computer Science, Purdue University（普渡大学计算机科学系）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Department Materials Science and Engineering, Ohio State University（俄亥俄州立大学材料科学与工程系）
Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultra or deep strong coupling, where the light-matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light-matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi mode…
