We report a novel hemispherical micro-cavity that is comprised of a planar integrated semiconductor distributed Bragg reflector (DBR) mirror, and an external, concave micro-mirror having a radius of curvature $50\mathrm{μm}$. The integrated DBR mirror containing quantum dots (QD), is designed to locate the QDs at an antinode of the field in order to maximize the interaction between the QD and the cavity. The concave micro-mirror, with high-reflectivity over a large solid-angle, creates a diffraction-limited (sub-micron) mode-waist at the planar mirror, leading to a large coupling constant between cavity mode and QD. The half-monolithic design gives more spatial and spectral tuning abilities, relatively to fully monolithic structures. This unique micro-cavity design will potentially enable us to both reach the cavity quantum electrodynamics (QED) strong coupling regime and realize the deterministic generation of single photons on demand.
We present a theoretical proposal for a physical implementation of entanglement concentration and purification protocols for two-mode squeezed microwave photons in circuit quantum electrodynamics (QED). First, we give the description of the cross-Kerr effect induced between two resonators in circuit QED. Then we use the cross-Kerr media to design the effective quantum nondemolition (QND) measurement on microwave-photon number. By using the QND measurement, the parties in quantum communication can accomplish the entanglement concentration and purification of nonlocal two-mode squeezed microwave…
Bell's inequality in three coupled quantum dots (QDs) within cavity QED, including Forster and exciton-phonon interactions, is investigated theoretically. For an initially entangled state, Bell's inequality is valid for certain times and violated for some other times. It is shown that the system moves from a product state to a entangled state and back again during it's time evolution.
We have measured the second-order correlation function of the cavity-QED microlaser output and observed a transition from photon bunching to antibunching with increasing average number of intracavity atoms. The observed correlation times and the transition from super- to sub-Poisson photon statistics can be well described by gain-loss feedback or enhanced/reduced restoring action against fluctuations in photon number in the context of a quantum microlaser theory and a photon rate equation picture. However, the theory predicts a degree of antibunching several times larger than that observed, wh…
We discuss the optimization of optical microcavity designs based on 2D photonic crystals for the purpose of strong coupling between the cavity field and a single neutral atom trapped within a hole. We present numerical predictions for the quality factors and mode volumes of localized defect modes as a function of geometric parameters, and discuss some experimental challenges related to the coupling of a defect cavity to gas-phase atoms.
In recent years, superconducting qubits show great potential in quantum computation. Hence, microwave photons become very interesting qubits for quantum information processing assisted by superconducting quantum computation. Here, we present the first protocol for the entanglement concentration on microwave photons, resorting to the cross-Kerr effect in circuit quantum electrodynamics (QED). Two superconducting transmission line resonators (TLRs) coupled to superconducting molecule with the N-type level structure induce the effective cross-Kerr effect for realizing the quantum nondemolition (Q…
Microwave photons have become very important qubits in quantum communication as the first quantum satellite has been launched successfully. Therefore, it is a necessary and meaningful task for ensuring the high security and efficiency of microwave-based quantum communication in practice. Here, we present an original polarization entanglement purification protocol for nonlocal microwave photons based on the cross-Kerr effect in circuit quantum electrodynamics (QED). Our protocol can solve the problem that the purity of maximally entangled states used for constructing quantum channels will decre…
Higher-order transitions can occur in the ultrastrong-coupling regime of circuit QED through virtual processes governed by the counter-rotating interactions. We propose a feasible way to probe higher-order transitions through the scattering of propagating microwave photons incident on the hybrid qubit-cavity system. The lineshapes in the scattering spectra can indicate the coherent interaction between the qubits and the cavity, and the higher-order transitions can be identified in the population spectra. We further find that if the coupling strengths between the two qubits and the cavity are t…
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 c…
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is,…
We explore applications of nonlinear circuit QED with a charge qubit inductively coupled to a microwave LC resonator in the photonic engineering and ultrastrong-coupling multiphoton quantum optics. Simply sweeping the gate-voltage bias achieves arbitrary Fock-state pulsed maser, where the single qubit plays the role of artificial gain medium. Resonantly pumping the parametric qubit-resonator interface leads to the squeezing of resonator field, which is utilizable to the quantum-limited microwave amplification. Moreover, upwards and downwards multiphoton quantum jumps may be observed in the ste…
We propose a scheme for generating entangled states for two superconducting quantum interference devices in a thermal cavity with the assistance of a microwave pulse.
We investigate a two-way cascaded cavity QED system consisting of microtoroidal resonators coupled through an optical fiber. Each microtoroidal cavity supports two counter-propagating whispering-gallery modes coupled to single atoms through their evanescent fields. We focus on a pair of atom-microtoroid systems and compute the spectrum of spontaneous emission into the fiber with one atom initially excited. Explicit results are presented for strong-coupling and bad-cavity regimes, where the latter allows the effective atom-atom interaction to be controlled through the atom-cavity coupling and d…
We propose a scheme for single-atom, quantum control of the direction of propagation of a coherent field incident, via a tapered fiber, upon a microtoroidal whispering-gallery-mode (WGM) resonator. The scheme involves overcoupling of the fiber-taper to the resonator and strong coupling of an atom to the evanescent field of the WGM, i.e., an atom-field coupling that exceeds the total WGM linewidth. In contrast to previous, related schemes that operate in the bad-cavity regime, the proposed scheme can operate effectively with much stronger incident fields, while also preserving their coherent na…
We study the nonlinear dynamics of an ensemble of cold trapped atoms with a hyperfine transition magnetically coupled to a resonant microwave cavity mode. Despite the minute single atom coupling one obtains strong coupling between collective hyperfine qubits and microwave photons enabling coherent transfer of an excitation between the long lived atomic qubit state and the mode. Evidence of strong coupling can be obtained from the cavity transmission spectrum even at finite thermal photon number. The system makes it possible to study further prominent collective phenomena such as superradiant d…
We theoretically propose a circuit QED system implemented with triple-leg stripline resonator (TSR). Unlikely from linear stripline resonator, the fundamental intra-cavity microwave modes of the TSR are two-fold degenerate. When a superconducting qubit is placed near one of the TSR legs, one fundamental mode is directly coupled to the qubit, while the other one remains uncoupled. Our system closely resembles an optical cavity QED system, where an atom in a cavity couples only to the incident photon with a specific polarization by placing a polarization beamsplitter in front of the optical cavi…
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…
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.
In order to examine whether or not the quantum phase transition of Dicke type exists in realistic systems, we revisit the model setup of the superconducting circuit QED from a microscopic many-body perspective based on the BCS theory with pseudo-spin presentation. By deriving the Dicke model with the correct charging terms from the minimum coupling principle, it is shown that the circuit QED system can exhibit superradiant quantum phase transition in the limit N\rightarrow\infty. The critical point could be reached at easiness by adjusting the extra parameters, the ratio of Josephson capacitan…
Quantum optical photodetection has occupied a central role in understanding radiation-matter interactions. It has also contributed to the development of atomic physics and quantum optics, including applications to metrology, spectroscopy, and quantum information processing. The quantum microwave regime, originally explored using cavities and atoms, is seeing a novel boost with the generation of nonclassical propagating fields in circuit quantum electrodynamics (QED). This promising field, involving potential developments in quantum information with microwave photons, suffers from the absence o…
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.
We analyze the magnetic dipole coupling of an ensemble of spins to a superconducting microwave stripline structure, incorporating a Josephson junction based transmon qubit. We show that this system is described by an embedded Jaynes-Cummings model: in the strong coupling regime, collective spin-wave excitations of the ensemble of electrons pick up the nonlinearity of the cavity mode, such that the two lowest eigenstates of the coupled spin-wave + microwave-cavity + Josephson-junction system define a hybrid two-level system. The proposal described here enables the use of spin ensembles as qubit…
The correction of errors is of fundamental importance for the development of contemporary computing devices and of robust communication protocols. In this paper we propose a scheme for the implementation of the three-qubit quantum repetition code, exploiting the interaction of Rydberg atoms with the quantized mode of a microwave cavity field. Quantum information is encoded within two circular Rydberg states of the atoms and encoding and decoding process are realized within two separate microwave cavities. We show that errors due to phase noise fluctuations could be efficiently corrected using …
Quantum mechanical effects at the macroscopic level were first explored in Josephson junction-based superconducting circuits in the 1980's. In the last twenty years, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review.…
The very small size of optical nonlinearities places wide ranging restrictions on the types of novel physics one can explore. For an ensemble of multi-level systems one can synthesize a large effective optical nonlinearity using quantum coherence effects but such non-linearities are technically extremely challenging to demonstrate at the single atom level. In this work we describe how a single artificial multi-level Cooper Pair Box molecule, interacting with a superconducting microwave coplanar waveguide resonator, when suitably driven, can generate extremely large optical nonlinearities at mi…
We present a complete fabrication study of an efficiently-coupled microring optical circuit tailored for cavity quantum electrodynamics (QED) with trapped atoms. The microring structures are fabricated on a transparent membrane with high in-vacuum fiber edge-coupling efficiency in a broad frequency band. In addition, a bus waveguide pulley coupler realizes critical coupling to the microrings at both of the cesium D-line frequencies, while high coupling efficiency is achieved at the cesium 'magic' wavelengths for creating a lattice of two-color evanescent field traps above a microring. The pres…
Based on a circuit QED qubit-cavity array a source of two-mode entangled microwave radiation is designed. Our scheme is rooted in the combination of external driving, collective phenomena and dissipation. On top of that the reflexion symmetry is broken via external driving permitting the appearance of chiral emission. Our findings go beyond the applications and are relevant for fundamental physics, since we show how to implement quantum lattice models exhibiting criticality driven by dissipation.
The spectrum of the cavity-QED microlaser/micromaser is expected to show distinctive features of the coherent light-matter interaction, which are obscured in the conventional Schawlow-Townes linewidth theory. However, the spectral studies has been limited to resonant atom-cavity interaction so far. Here we consider the dispersive interaction in the off-resonance case, from which we uncover a quantum frequency pulling effect in the microlaser/micromaser spectrum. We present a quantum theory of the spectrum which introduces the notion of a frequency-pulling distribution associated with the photo…
We generalize the Power-Zineau-Woolley transformation to obtain a canonical Hamiltonian of cavity quantum electrodynamics for arbitrary geometry of boundaries. This Hamiltonian is free from the A-square term and the instantaneous Coulomb interaction between distinct atoms. The single-mode models of cavity QED (Dicke, Tavis-Cummings, Jaynes-Cummings) are justified by a term by term mapping to the proposed microscopic Hamiltonian. As one straightforward consequence, the basis of no-go argumentations concerning the Dicke phase transition with atoms in electromagnetic fields dissolves.
We refine a QED-cavity model of microtubules (MTs), proposed earlier by two of the authors (N.E.M. and D.V.N.), and suggest mechanisms for the formation of biomolecular mesoscopic coherent and/or entangled quantum states, which may avoid decoherence for times comparable to biological characteristic times. This refined model predicts dissipationless energy transfer along such "shielded" macromolecules at near room temperatures as well as quantum teleportation of states across MTs and perhaps neurons.
We propose a realistic scheme of generating a traveling odd Schr$ö$dinger cat state and a generalized entangled coherent state in circuit quantum electrodynamics (circuit-QED). A squeezed vacuum state is used as initial resource of nonclassical states, which can be created through a Josephson traveling-wave parametric amplifier, and travels through a transmission line. Because a single-photon subtraction from the squeezed vacuum gives with very high fidelity an odd Schr$ö$dinger cat state, we consider a specific circuit-QED setup consisting of the Josephson amplifier creating the traveling res…
We propose a circuit QED platform and protocol to generate microwave photonic tensor network states deterministically. We first show that using a microwave cavity as ancilla and a transmon qubit as emitter is a good platform to produce photonic matrix product states. The ancilla cavity combines a large controllable Hilbert space with a long coherence time, which we predict translates into a high number of entangled photons and states with a high bond dimension. Going beyond this paradigm, we then consider a natural generalization of this platform, in which several cavity-qubit pairs are couple…
Hybrid quantum systems based on spin ensembles coupled to superconducting microwave cavities are promising candidates for robust experiments in cavity quantum electrodynamics (QED) and for future technologies employing quantum mechanical effects. Currently the main source of decoherence in these systems is inho- mogeneous spin broadening, which limits their performance for the coherent transfer and storage of quantum information. Here we study the dynamics of a superconducting cavity strongly coupled to an ensemble of nitrogen-vacancy centers in diamond. We experimentally observe for the first…
We present results of numerical investigation of a microscopic dynamics of a two-level atom embedded into a ``linear crystal'' of other two-level atoms. These additional atoms play a role of a material media. All atoms interact with a multimode cavity field. We study how the decay of the initially excited atom is affected by the presence of material media and spectral properties of the cavity field.
Using resonant interaction of three Rydberg atoms with a single-mode microwave cavity, we consider a realization of three-qubit Grover search algorithm in the presence of weak cavity decay, based on a previous idea for three-qubit quantum gate [Phys. Rev. A 73, 064304 (2006)]. We simulate the searching process under the influence of the cavity decay and show that our scheme could be achieved efficiently to find the marked state with high fidelity. The required operations are very close to the reach with current cavity QED techniques.
In this article we discuss two schemes of teleportation of atomic states. In the first scheme we consider atoms in a three-level cascade configuration and in the second scheme we consider atoms in a three-level lambda configuration. The experimental realization proposed makes use of cavity Quatum Electrodynamics involving the interaction of Rydberg atoms with a micromaser cavity prepared in a state $|ψ>_{C}=(|0> +|1>)/\sqrt{2}$
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.
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has im…
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…
Future quantum technology relies crucially on building quantum networks with high fidelity. To achieve this challenging goal, it is of utmost importance to connect single quantum systems in a way such that their emitted single-photons overlap with the highest possible degree of coherence. This requires perfect mode overlap of the emitted light of different emitters, which necessitates the use of single mode fibers. Here we present an advanced manufacturing approach to accomplish this task: we combine 3D printed complex micro-optics such as hemispherical and Weierstrass solid immersion lenses a…
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…
We theoretically study the realization of a multi-qubit refined Deutsch-Jozsa (DJ) algorithm using resonant interaction of many Rydberg atoms with a single-mode microwave cavity, in which the multi-qubit controlled phase gates could be accomplished efficiently. We show how to achieve a multi-qubit refined DJ algorithm in high fidelity, even in the case of a weak cavity decay and some imperfection. We argue that the required operations in our scheme are almost within the present experimental possibilities.
We study analytically the dynamics of cavity QED nodes in a practical quantum network. Given a single 3-level $Λ$-type atom or quantum dot coupled to a micro-cavity, we derive several necessary and sufficient criteria for the coherent trapping and generation of a single photon pulse with a given waveform to be realizable. We prove that these processes can be performed with practical hardware -- such as cavity QED systems which are operating deep in the weak coupling regime -- given a set of restrictions on the single-photon pulse envelope. We systematically study the effects of spontaneous emi…
We propose an interface between the spin of a photon and the spin of an electron confined in a quantum dot embedded in a microcavity operating in the weak coupling regime. This interface, based on spin selective photon reflection from the cavity, can be used to construct a CNOT gate, a multi-photon entangler and a photonic Bell-state analyzer. Finally, we analyze experimental feasibility, concluding that the schemes can be implemented with current technology.
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.
Circuit quantum electrodynamics ('circuit QED') describes the quantum mechanics and quantum field theory of superconducting electrical circuits operating in the microwave regime near absolute zero temperature. It is the analog of cavity QED in quantum optics with the role of the atoms being played by superconducting qubits. The present lecture notes focus primarily on novel quantum states that can be produced and measured using the strong coupling between an artificial atom and one or more cavities. Of particular importance are Schrodinger cat states of photons. Despite long being considered e…
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…
We explore the dynamics of the entanglement in a semiconductor cavity QED containing a quantum well. We show the presence of sudden birth and sudden death for some particular sets of the system parameters.
We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
We present a method to enact a deterministic, measurement-free, optically generated controlled-phase gate on two qubits defined by single electrons trapped in large-area quantum dots in a planar microcavity. This method is robust to optical quantum dot inhomogeneity, requires only a modest-$Q$ planar cavity, employs only a single laser pulse, and allows the integration of many entangled qubits on one semiconductor chip. We present the gate in the contexts of both adiabatic evolution and geometric phases, and calculate the degradation of performance in the presence of both spontaneous emission …
The high density Frenkel exciton which interacts with a single mode microcavity field is dealed with in the framework of the q-deformed boson. It is shown that the q-defomation of bosonic commutation relations is satisfied naturally by the exciton operators when the low density limit is deviated. An analytical expression of the physical spectrum for the exciton is given by using of the dressed states of the cavity field and the exciton. We also give the numerical study and compare the theoretical results with the experimental results
We present a decoherence-based interpretation for the quantum Zeno effect (QZE) where measurements are dynamically treated as dispersive couplings of the measured system to the apparatus, rather than the von Neumann's projections. It is found that the explicit dependence of the survival probability on the decoherence time quantitatively distinguishes this dynamic QZE from the usual one based on projection measurements. By revisiting the cavity-QED experiment of the QZE [J. Bernu, et al., Phys. Rev. Lett, 101, 180402 (2008)], we suggest an alternative scheme to verify our theoretical considerat…
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 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…
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…
By driving a dispersively coupled qubit-resonator system, we realize an "impedance-matched" $Λ$ system that has two identical radiative decay rates from the top level and interacts with a semi-infinite waveguide. It has been predicted that a photon input from the waveguide deterministically induces a Raman transition in the system and switches its electronic state. We confirm this through microwave response to a continuous probe field, observing near-perfect ($99.7\%$) extinction of the reflection and highly efficient ($74\%$) frequency down-conversion. These proof-of-principle results lead to…
