We propose an architecture for a high-fidelity deterministic controlled-phase gate between two photonic qubits using bulk optical nonlinearities in near-term feasible photonic integrated circuits. The gate is enabled by converting travelling continuous-mode photons into stationary cavity modes using strong classical control fields that dynamically change the cavity-waveguide coupling rate. This process limits the fidelity degrading noise pointed out by Shapiro [J. Shapiro, Phys. Rev. A, 73, 2006] and Gea-Banacloche [J. Gea-Banacloche, Phys. Rev. A, 81, 2010]. We show that high-fidelity gates can be achieved with self-phase modulation in $χ^{\scriptscriptstyle(3)}$ materials as well as second-harmonic generation in $χ^{\scriptscriptstyle(2)}$ materials. The gate fidelity asymptotically approaches unity with increasing storage time for a fixed duration of the incident photon wave packet. Further, dynamically coupled cavities enable a trade-off between errors due to loss and wave packet distortions since loss does not affect the ability to emit wave packets with the same shape as the incoming photons. Our numerical results show that gates with $99\%$ fidelity are feasible with near-term improvements in cavity loss using LiNbO$_3$ or GaAs.
We study theoretically the interaction between two photons in a nonlinear cavity. The photons are loaded into the cavity via a method we propose here, in which the input/output coupling of the cavity is effectively controlled via a tunable coupling to a second cavity mode that is itself strongly output-coupled. Incoming photon wave packets can be loaded into the cavity with high fidelity when the timescale of the control is smaller than the duration of the wave packets. Dynamically coupled cavities can be used to avoid limitations in the photon-photon interaction time set by the delay-bandwidt…
Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quantum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off-resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number-dependent (PND) Hamiltonian for the cavities while minimizing the operation errors. The engineered Hamiltonian admits various app…
We study the properties of an array of QED-cavities coupled by nonlinear elements in the presence of photon leakage and driven by a coherent source. The main effect of the nonlinear couplings is to provide an effective cross-Kerr interaction between nearest-neighbor cavities. Additionally, correlated photon hopping between neighboring cavities arises. We provide a detailed mean-field analysis of the steady-state phase diagram as a function of the system parameters, the leakage, and the external driving, and show the emergence of a number of different quantum phases. A photon crystal associated…
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.
A system of two coupled cavities with $N-1$ photons is shown to be dynamically equivalent to an array of $N$ coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport en…
Single excitons in semiconductor microcavities represent a solid-state and scalable platform for cavity quantum electrodynamics (c-QED), potentially enabling an interface between flying (photon) and static (exciton) quantum bits in future quantum networks. While both single-photon emission and the strong coupling regime have been demonstrated, further progress has been hampered by the inability to control the coherent evolution of the c-QED system in real time, as needed to produce and harness charge-photon entanglement. Here, using the ultrafast electrical tuning of the exciton energy in a ph…
We introduce a method for calculating the stationary state of a translation invariant array of weakly coupled cavities in the presence of dissipation and coherent as well as incoherent drives. Instead of computing the full density matrix our method directly calculates the correlation functions which are relevant for obtaining all local quantities of interest. It considers an expansion of the correlation functions and their equations of motion in powers of the photon tunneling rate between adjacent cavities, leading to an exact second order solution for any number of cavities. Our method provid…
In our previous paper [Phys. Rev. A 84, 042303 (2011)], we proposed an efficient 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 controlled-NOT gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to con…
We show that highly confined superfluid films are extremely nonlinear mechanical resonators, offering the prospect to realize a mechanical qubit. Specifically, we consider third-sound surface waves, with nonlinearities introduced by the van der Waals interaction with the substrate. Confining these waves to a disk, we derive analytic expressions for the cubic and quartic nonlinearities and determine the resonance frequency shifts they introduce. We predict single-phonon shifts that are three orders of magnitude larger than in current state-of-the-art nonlinear resonators. Combined with the exqu…
Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum operations, static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Here we study theoretical models of nonlinear oscillators describing superconducting quantum circuits with asymmetric Josephson-junctions loops. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff…
We investigate non-equilibrium phase transitions for driven atomic ensembles, interacting with a cavity mode, coupled to a Markovian dissipative bath. In the thermodynamic limit and at low-frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path integral approach, that allows us to study physically relevant nonli…
In this paper we reveal the rich ground-state properties induced by the strong nonlinear atom-photon interaction, which has been found in the recent experiment about a Bose-Einstein condensate coupling with a high-finesse cavity [Nature (London) 464, 1301 (2010)]. Two detuning-dependent phase diagrams are revealed by investigating the experimentally-measurable atomic population. In particular, two new quantum phase transitions from the superradiant phase or the normal phase to a dynamically-unstable phase are predicted in the blue detuning, and moreover, the three-phase coexistence points are …
Enhancing optical nonlinearities so that they become appreciable on the single photon level and lead to nonclassical light fields has been a central objective in quantum optics for many years. After this has been achieved in individual micro-cavities representing an effectively zero-dimensional volume, this line of research has shifted its focus towards engineering devices where such strong optical nonlinearities simultaneously occur in extended volumes of multiple nodes of a network. Recent technological progress in several experimental platforms now opens the possibility to employ the system…
Efficient entanglement preservation in open quantum systems is a crucial scope towards a reliable exploitation of quantum resources. We address this issue by studying how two-qubit entanglement dynamically behaves when two atom qubits move inside two separated identical cavities. The moving qubits independently interact with their respective cavity. As a main general result, we find that under resonant qubit-cavity interaction the initial entanglement between two moving qubits remains closer to its initial value as time passes compared to the case of stationary qubits. In particular, we show t…
Dynamically suppressing cavity dephasing induced by frequency fluctuations of a coupled nonlinear mode
Northwestern University（西北大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Amazon Center for Quantum Computing（亚马逊量子计算中心）；Stanford University（斯坦福大学）
High-Q microwave cavity modes coupled to transmon ancillas provide a hardware-efficient platform for quantum computing. Due to their coupling, the cavity modes inherit finite nonlinearity from the transmons. In this work, we theoretically and experimentally investigate how an off-resonant drive on the transmon ancilla modifies the nonlinearities of cavity modes in qualitatively different ways, depending on the interrelation among cavity-transmon detuning, drive-transmon detuning and transmon anharmonicity. For a cavity-transmon detuning that is smaller than or comparable to the drive-transmon …
We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the Von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can be generated also in the limit where the nonlinearity is much smaller than the losses, contrarily to common expectations. Quantum correlations in this case arise from interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize in particular two systems: a linear chain of…
We study theoretically two-photon states in a periodic array of coupled cavities with both on-site and nonlocal Kerr-type nonlinearities. In the absence of nonlinearity the structure is topologically trivial and possesses no edge states. The interplay of two nonlinear interaction mechanisms described by the extended Hubbard model facilitates formation of edge states of bound photon pairs. Numerical and exact analytical results for the two-photon wave functions are presented. Our findings thus shed light onto the edge states of composite particles and their localization properties.
We present a joint theoretical and experimental characterization of thermo-refractive noise in high quality factor ($Q$), small mode volume ($V$) optical microcavities. Analogous to well-studied stability limits imposed by Brownian motion in macroscopic Fabry-Perot resonators, microcavity thermo-refractive noise gives rise to a mode volume-dependent maximum effective quality factor. State-of-the-art fabricated microcavities are found to be within one order of magnitude of this bound. We confirm the assumptions of our theory by measuring the noise spectrum of high-$Q/V$ silicon photonic crystal…
Optomechanics concerns with the coupling between optical cavities and mechanical resonators. Most early works are concentrated in the physics of optomechanics in the small-displacement regime and consider one single optical cavity mode participating in the optomechanical coupling. In this paper, we focus on optomechanics in the extremely-large-amplitude regime in which a mechanical resonator is coupled with multiple optical cavity modes during the oscillation. We explicitly show that the mechanical resonator can present self-sustained oscillations in a novel way with limit cycles in the shape …
Intuition dictates that a very long, very thin cavity (e.g., a fiber optic cable) could perhaps be modeled as an approximately one dimensional system. In this paper we rigorously explore the validity of such intuition from the perspective of a localized probe coupling to a quantum field inside a cavity (e.g., an atom or an Unruh-DeWitt particle detector in a fiber optic cable). To do so, we introduce the notion of subfield decomposition in which a $D+1$ dimensional quantum field in an axially-symmetric cavity can be reduced to an infinite collection of uncoupled, massive $1+1$ dimensional fiel…
When atoms scatter photons from a transverse laser into a high-finesse optical cavity, they form crystalline structures which maximize the intracavity light field and trap the atoms in the ordered array. Stable organization occurs when the laser field amplitude exceeds a certain threshold. For planar single-mode cavities there exist two equivalent possible atomic patterns, which determine the phase of the intracavity light field. Under these premises, we show that the effect of an additional laser pumping the cavity makes one pattern more favorable than the other and that it can dynamically fo…
Mode locking in lasers is a collective effect, where due to a weak coupling a large number of frequency modes lock their phases to oscillate in unison, forming an ultrashort pulse in time. We demonstrate an analogous collective effect in coupled parametric oscillators, which we term "pairwise mode-locking", where many pairs of modes with twin frequencies (symmetric around the center carrier) oscillate simultaneously with a locked phase-sum, while the phases of individual modes remain undefined. Thus, despite being broadband and multimode, the emission is not pulsed and lacks first-order cohere…
We study a 1D chain of non-interacting bosonic cavities which are subject to nearest-neighbour parametric driving. With a suitable choice of drive phases, this model is strongly analogous to the celebrated Kitaev chain model of a 1D p-wave superconductor. The system exhibits phase-dependent chirality: photons propagate and are amplified in a direction that is determined by the phase of the initial drive or excitation. Further, we find a drastic sensitivity to boundary conditions: for a range of parameters, the boundary-less system has only delocalized, dynamically unstable modes, while a finit…
Optically-Induced Modulation and Programming of Diamond Photonic Cavities
Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Center of Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）；Photonics Research Group, Department of Information Technology (INTEC), Ghent University - IMEC（根特大学信息技朮系光子研究组（与IMEC联合））；University of Stuttgart（斯图加特大学）
We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-$\frac{1}{2}$ model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results…
A model for a controlled single-photon beam-splitter is proposed and analysed. It consists of two crossed optical-cavities with overlapping waists, dynamically coupled to a single flying atom. The system is shown to route a single photon with near-unity efficiency in an effective "weak-coupling" regime. Furthermore, two such nodes, forming a segment of a quantum network, are shown to perform several controlled quantum operations. All one-qubit operations involve a transfer of a photon from one cavity to another in a single node, while two-qubit operations involve transfer from one node to a ne…
The on-chip generation of non-classical states of light is a key-requirement for future optical quantum hardware. In solid-state cavity quantum electrodynamics, such non-classical light can be generated from self-assembled quantum dots strongly coupled to photonic crystal cavities. Their anharmonic strong light-matter interaction results in large optical nonlinearities at the single photon level, where the admission of a single photon into the cavity may enhance (photon-tunnelling) or diminish (photon-blockade) the probability for a second photon to enter the cavity. Here, we demonstrate that …
The enormous progress in controlling quantum optical and atomic systems has prompted ideas for new experimental realizations of strongly correlated many-body systems operating with light. These systems consist of photons confined in optical cavities, which interact strongly with atoms or atomiclike structures. Due to the interaction between the two particle species optical nonlinearities appear, leading to a quantum phase transition from Mott to superfluid phase. Here, we address the Tavis-Cummings lattice model, which describes light-matter systems containing multiple atomiclike structures in…
Mobile light scatterers in a high-Q optical cavity transversely illuminated by laser light close to a cavity resonance form ordered patterns, which maximize light scattering into the cavity and induce optical self-trapping. We show that a generalized form of such crystallization dynamics appears in multicolored pump fields with several cavity modes. Here the particles arrange in spatial patterns maximizing total light collection into the resonator. For changing input frequencies and strengths the particles dynamically adapt to the current illumination. Interestingly the system keeps some memor…
We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or rais…
