We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded in a waveguide. Our analysis reveals strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering such as superradiant, subradiant, and twilight states, being a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to a storage and processing of quantum information.
Superradiance and subradiance concerning enhanced and inhibited collective radiation of an ensemble of atoms have been a central topic in quantum optics. However, precise generation and control of these states remain challenging. Here we deterministically generate up to 10-qubit superradiant and 8-qubit subradiant states, each containing a single excitation, in a superconducting quantum circuit with multiple qubits interconnected by a cavity resonator. The $\sqrt{N}$-scaling enhancement of the coupling strength between the superradiant states and the cavity is validated. By applying appropriat…
We study theoretically driven quantum dynamics in periodic arrays of two-level qubits coupled to the waveguide. We demonstrate, that strongly subradiant eigenstates of the master equation for the density matrix emerge under strong coherent driving for arrays with the anti-Bragg periods $d=λ/4,3λ/4$... This happens even though are no such states at low driving powers. Thus, our findings show that in the quantum nonlinear regime the domain of existence of subradiant states expands beyond conventional subwavelength structures. These driven states are directly manifested in long-living quantum cor…
We propose a realization of a scalable, high-performance quantum processor whose qubits are represented by the ground and subradiant states of effective dimers formed by pairs of two-level systems coupled by resonant dipole-dipole interaction. The dimers are implanted in low-temperature solid host material at controllable nanoscale separations. The two-qubit entanglement either relies on the coherent excitation exchange between the dimers or is mediated by external laser fields.
Transitions between quantum states by photon absorption or emission are intimately related to symmetries of the system which lead to selection rules and the formation of dark states. In a circuit quantum electrodynamics setup, in which two resonant superconducting qubits are coupled through an on-chip cavity and driven via the common cavity field, one single-excitation state remains dark. Here, we demonstrate that this dark state can be excited using local phase control of individual qubit drives to change the symmetry of the driving field. We observe that the dark state decay via spontaneous …
We propose a tunable coupler consisting of N fixed-frequency qubits, which can tune and even amplify the effective interaction between two superconducting quantum circuits. The tuning range of the interaction is proportional to N, with a minimum value of zero and a maximum that can exceed the physical coupling rates between the coupler and the circuits. The effective coupling rate is determined by the collective magnetic quantum number of the qubit ensemble, which takes only discrete values and is free from collective decay and decoherence. Using single-photon pi-pulses, the coupling rate can …
We propose to generate the multiphoton subradiant states and investigate their fluorescences in an array of two-level atoms. These multiphoton states are created initially from the timed-Dicke states. Then we can use either a Zeeman or Stark field gradient pulse to imprint linearly increasing phases on the atoms, and this phase-imprinting process unitarily evolves the system to the multiphoton subradiant states. The fluorescence engages a long-range dipole-dipole interaction which originates from a system-reservoir coupling in the dissipation. We locate some of the subradiant multiphoton state…
The properties of coupled emitters can differ dramatically from those of their individual constituents. Canonical examples include sub- and super-radiance, wherein the decay rate of a collective excitation is reduced or enhanced due to correlated interactions with the environment. Here, we systematically study the properties of collective excitations for regularly spaced arrays of quantum emitters coupled to a one-dimensional (1D) waveguide. We find that, for low excitation numbers, the modal properties are well-characterized by spin waves with a definite wavevector. Moreover, the decay rate o…
The entanglement dynamics of a laser-pumped two-level quantum dot pair is investigated in the steady-state. The closely spaced two-level emitters, embedded in a semiconductor substrate, interact with both the environmental vacuum modes of the electromagnetic field reservoir as well as with the lattice vibrational phonon thermostat. We have found that the entanglement among the pair's components is substantially enhanced due to presence of the phonon subsystem. The reason is phonon induced decay among the symmetrical and antisymmetrical two-qubit collective states and, consequently, the populat…
We calculate the radiative properties for a linear dipole-coupled chain of qubits. Using the explicit energy eigenstates of the system, we find the radiation patterns for spontaneous transitions from the one-photon eigenstates to the ground state of the system. We show that depending on the excitation of a specific atom, the radiation tends to be focused either along or perpendicular to the chain. We conclude with a derivation of the total decay rate of the one-photon eigenstates, and find the interesting result that for systems where the photon wavenumber is not much larger than the interatom…
We consider a one-dimensional chain of N equidistantly spaced noninteracting qubits embedded in an open waveguide. In the frame of single-excitation subspace, we systematically study the evolution of qubits amplitudes if the only qubit in the chain was initially excited. We show that the temporal dynamics of qubits amplitudes crucially depend on the value of kd, where k is the wave vector, d is a distance between neighbor qubits. If kd is equal to an integer multiple of $π$, then the qubits are excited to a stationary level which scales as SN^{-1}S. We show that in this case, it is the dark st…
Waveguide quantum electrodynamics offers a wide range of possibilities to effectively engineer interactions between artificial atoms via a one-dimensional open waveguide. While these interactions have been experimentally studied in the few qubit limit, the collective properties of such systems for larger arrays of qubits in a metamaterial configuration has so far not been addressed. Here, we experimentally study a metamaterial made of eight superconducting transmon qubits with local frequency control coupled to the mode continuum of a waveguide. By consecutively tuning the qubits to a common r…
We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line. Similarly to the atomic cases, RDDI comes from exchange of virtual photons of the unexcited modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incide…
We study the evolution of qubits amplitudes in a one-dimensional chain consisting of three equidistantly spaced noninteracting qubits embedded in an open waveguide. The study is performed in the frame of single-excitation subspace, where the only qubit in the chain is initially excited. We show that the dynamics of qubits amplitudes crucially depend on the value of $kd$, where $k$ is the wave vector, $d$ is a distance between neighbor qubits. If $kd$ is equal to an integer multiple of $π$, then the qubits are excited to a stationary level. In this case, it is the dark states which prevent qubi…
We consider the inelastic scattering of two photons from two qubits separated by an arbitrary distance $R$ and coupled to a one-dimensional transmission line. We present an exact, analytical solution to the problem, and use it to explore a particular configuration of qubits which is transparent to single-photon scattering, thus highlighting non-Markovian effects of inelastic two-photon scattering: Strong two-photon interference and momentum dependent photon (anti-)bunching. This latter effect can be seen as an inelastic generalization of the Hong--Ou--Mandel effect.
We study the dynamics of a charge qubit, consisting of a single electron in a double well potential, coupled to a point-contact (PC) electrometer using the quantum trajectories formalism. In contrast with previous work, our analysis is valid for arbitrary source-drain bias across the PC, but is restricted to the sub-Zeno limit. We find that the dynamics is strongly affected by inelastic tunnelling processes in the PC. These processes reduce the efficiency of the PC as a qubit readout device, and induce relaxation even when the source-drain bias is zero. We show that the sub-Zeno dynamics are d…
Random scattering of photons in disordered one-dimensional solids gives rise to an exponential suppression of transmission, which is known as Anderson localization. Here, we experimentally study Anderson localization in a superconducting waveguide quantum electrodynamics system comprising eight individually tunable qubits coupled to a photonic continuum of a waveguide. Employing the qubit frequency control, we artificially introduce frequency disorder to the system and observe an exponential suppression of the transmission coefficient in the vicinity of its subradiant dark modes. The localizat…
Subradiant excited states in finite chains of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and controlled photon manipulation. Typically, states storing multiple excitations exhibit fermionic correlations and are thus characterized by an anti-symmetric wavefunction, which makes them hard to prepare experimentally. Here we identify a class of quasi-localized dark states with up to half of the qubits excited, which appear for lattice constants that are an integer multiple of the guided-mode wavelength. They allow for a high-fidelity…
Collective dressed states for inelastic light scattering by atomic ensembles
Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Nanyang Technological University（南洋理工大学）；MajuLab（马久实验室）；Université Côte d’Azur（蔚蓝海岸大学）；Sorbonne Université（索邦大学）；National University of Singapore（新加坡国立大学）；Center for Quantum Technologies（量子技术中心）
We present a time-dependent quantum algorithm for nuclear inelastic scattering in the time-dependent basis function on qubits approach. This algorithm aims to quantum simulate a subset of the nuclear inelastic scattering problems that are of physical interest, in which the internal degrees of freedom of the reaction system are excited by time-dependent external interactions. We expect that our algorithm will enable an exponential speedup in simulating the dynamics of the subset of the inelastic scattering problems, which would also be advantageous for the applications to more complicated scatt…
The ability to generate single photons is not only an ubiquitous tool for scientific exploration with applications ranging from spectroscopy and metrology to quantum computing, but also an important proof of the underlying quantum nature of a physical process. In the microwave regime, emission of anti-bunched radiation has so far relied on coherent control of Josephson qubits, where precisely calibrated microwave pulses are needed, and the achievable bandwidth is limited by the anharmonicity of the qubit. Here, we demonstrate the operation of a bright on-demand source of quantum microwave radi…
We study the dynamics of a charge qubit, consisting of a single electron in a double well potential coupled to a point-contact (PC) electrometer, using the quantum trajectories formalism. Contrary to previous predictions, we show formally that, in the sub-Zeno limit, coherent oscillations in the detector output are suppressed, and the dynamics is dominated by inelastic processes in the PC. Furthermore, these reduce the detector efficiency and induce relaxation even when the source-drain bias is zero. This is of practical significance since it means the detector will act as a source of decohere…
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of $N$, $M$, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the Matrix Product States technique. Both the time evolution for the field and qubits is computed. The nonlinear character (as a function of $N/M$) depends on the computed observable. While perfe…
Nature sets fundamental limits regarding how accurate the amplification of analog signals may be. For instance, a linear amplifier unavoidably adds some noise which amounts to half a photon at best. While for most applications much higher noise levels are acceptable, the readout of microwave quantum systems, such as spin or superconducting qubits, requires noise as close as possible to this ultimate limit. To date, it is approached only by parametric amplifiers exploiting non-linearities in superconducting circuits and driven by a strong microwave pump tone. However, this microwave drive makes…
Self-assembled quantum dots are ideal structures in which to test theories of open quantum systems: Confined exciton states can be coherently manipulated and their decoherence properties are dominated by interactions with acoustic phonons. We here describe the interaction of a pair of un-coupled, driven, quantum dot excitons with a common phonon environment, and find that this coupling effectively generates two kinds of interaction between the two quantum dots: An elastic coupling mediated by virtual phonons and an inelastic coupling mediated by real phonons. We show that both of these interac…
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify by showing how to teleport an unknown quantum state and how to efficiently prepare graph states for the implementation of measurement-based quantum computation.
We investigate quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the emitted photonic states, in the framework of the spin-boson model Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we…
We study the scattering of photons by a two-level system ultrastrongly coupled to a one-dimensional waveguide. Using a combination of the polaron transformation with scattering theory we can compute the one-photon scattering properties of the qubit for a broad range of coupling strengths, estimating resonance frequencies, lineshapes and linewidths. We validate numerically and analytically the accuracy of this technique up to $α=0.3$, close to the Toulouse point $α=1/2$, where inelastic scattering becomes relevant. These methods model recent experiments with superconducting circuits [P. Forn-D{…
Instantons, spacetime-localized quantum field tunneling events, are ubiquitous in correlated condensed matter and high energy systems. However, their direct observation through collisions with conventional particles has not been considered possible. We show how recent advances in circuit quantum electrodynamics, specifically, the realization of galvanic coupling of a transmon qubit to a high-impedance transmission line, allows the observation of inelastic collisions of single microwave photons with instantons (phase slips). We develop a formalism for calculating the photon-instanton cross sect…
Suppression of coherent light scattering in a three-dimensional atomic array
Massachusetts Institute of Technology（麻省理工学院）；Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；MIT-Harvard Center for Ultracold Atoms（MIT-哈佛超冷原子中心）
The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using Matrix Product States. It is found that the scattering is strongly influenced by the single- and multi-photon dressed bound states present in the system. In the ultrastrong coupling regime a new channel for inelastic scattering appears, where an incident photon deposits energy into the qubit, exciting a photon-bound…
