The coherent interaction of Rydberg helium atoms with microwave fields in a $λ/4$ superconducting coplanar waveguide resonator has been exploited to probe the spectral characteristics of an individual resonator mode. This was achieved by preparing the atoms in the 1s55s$^3$S$_1$ Rydberg level by resonance enhanced two-color two-photon excitation from the metastable 1s2s$^3$S$_1$ level. The atoms then travelled over the resonator in which the third harmonic microwave field, at a frequency of $ω_{\mathrm{res}}=2π\times19.556$ GHz, drove the two-photon 1s55s$^3$S$_1\rightarrow$1s56s$^3$S$_1$ transition. By injecting a sequence of Ramsey pulses into the resonator, and monitoring the coherent evolution of the Rydberg state population by state-selective pulsed electric field ionization as the frequency of the microwave field was tuned, spectra were recorded that allowed the resonator resonance frequency and quality factor to be determined with the atoms acting as microscopic quantum sensors.
We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The many-body dynamics is governed by an Ising-type Hamiltonian with long range interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities.
We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions. In contrast to many prior proposals, our scheme operates comfortably within experimentally measured lifetimes, and accesses a regime where quantum superpositions are crucial. The key idea is to build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, for which we derive an exact solution. Due to the structure of Rydberg interactions, the dynamics differs significantly …
We study ensembles of Rydberg atoms in a confined electromagnetic environment such as provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle-particle couplings range from the typical van der Waals $r^{-6}$ behavior to $r^{-3}$ and to $r$-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for consider…
We present an experimental study of cavity assisted Rydberg atom electromagnetically induced transparency (EIT) using a high-finesse optical cavity ($F \sim 28000$). Rydberg atoms are excited via a two-photon transition in a ladder-type EIT configuration. A three-peak structure of the cavity transmission spectrum is observed when Rydberg EIT is generated inside the cavity. The two symmetrically spaced side peaks are caused by bright-state polaritons, while the central peak corresponds to a dark-state polariton. Anti-crossing phenomenon and the effects of mirror adsorbate electric fields are st…
A Rydberg atom array coupled to a high-cooperativity optical cavity
University of California, Berkeley（加州大学伯克利分校）；Challenge Institute for Quantum Computation, University of California, Berkeley（加州大学伯克利分校量子计算挑战研究所）；Columbia University（哥伦比亚大学）；Oratomic
This work reports on the real-time detection of internal-state dynamics of cold Rb$^{87}$ atoms being excited to the $30D_{5/2}$ Rydberg state via two-photon excitation. A mesoscopic cloud of atoms is overlapped with the mode volume of a confocal optical cavity and optically pumped by two laser beams transverse to the cavity axis. The excitation to Rydberg states changes the collective atom-cavity coupling, which is detected by monitoring the light transmitted through the cavity while being weakly driven. In addition to the damped coherent excitation dynamics and the decay back to the ground s…
Rydberg atoms are at the core of an increasing number of experiments, which frequently rely on destructive detection methods, such as field ionization. Here, we present an experimental realization of single-shot non-destructive detection of ensembles of helium Rydberg atoms. We use the dispersive frequency shift of a superconducting microwave cavity interacting with the ensemble. By probing the transmission of the cavity and measuring the change in its phase, we determine the number of Rydberg atoms or the populations of Rydberg quantum states when the ensemble is prepared in a superposition. …
In recent years the interest in studying interactions of Rydberg atoms or ensembles thereof with optical and microwave frequency fields has steadily increased, both in the context of basic research and for potential applications in quantum information processing. We present measurements of the dispersive interaction between an ensemble of helium atoms in the 37s Rydberg state and a single resonator mode by extracting the amplitude and phase change of a weak microwave probe tone transmitted through the cavity. The results are in quantitative agreement with predictions made on the basis of the d…
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Technische Universität München（慕尼黑工业大学）
We demonstrate hybridization of optical cavity photons with atomic Rydberg excitations using electromagnetically induced transparency (EIT). The resulting dark state Rydberg polaritons exhibit a compressed frequency spectrum and enhanced lifetime indicating strong light-matter mixing. We study the coherence properties of cavity Rydberg polaritons and identify the generalized EIT linewidth for optical cavities. Strong collective coupling suppresses polariton losses due to inhomogeneous broadening, which we demonstrate by using different Rydberg levels with a range of polarizabilities. Our resul…
We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity. The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity. Heralding enables high-fidelity entanglement even for a cavity of moderate quality. For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few $μ$s, enabling the any-to-any entanglement of 20 ion ch…
We investigate a new laser scheme by using Ramsey separated-field technique with bad cavity. By studying the linewidth of the stimulated-emission spectrum of this kind of laser inside the cavity, we find its linewidth is more than two orders of magnitude narrower than atomic natural linewidth, and it is far superior to that of conventional optical Ramsey method and any other available subnatural linewidth spectroscopy at present. Since any cavity related noise is reduced to cavity-pulling effect in bad cavity laser, this Ramsey laser provides the possibility of precision subnatural linewidth s…
We propose how to achieve strong photon antibunching effect in a cavity-QED system coupled with two Rydberg-Rydberg interaction atoms. Via calculating the equal time second order correlation function g(2)(0), we find that the unconventional photon blockade and the conventional photon blockade appear in the atom-driven scheme, and they are both significantly affected by the Rydberg-Rydberg interaction. We also find that under appropriate parameters, the photon antibunching and the mean photon number can be significantly enhanced by combining the conventional photon blockade and the unconvention…
In a previous letter we studied the giant optical nonlinearities of a Rydberg atomic medium within an optical cavity, in the Schwinger-Keldysh formalism. In particular, we calculated the non-linear contributions to the spectrum of the light transmitted through the cavity. In this article we spell out the essential details of this calculation, and we show how it can be extended to higher input photon numbers, and higher order correlation functions. As a relevant example, we calculate and discuss the three-photon correlation function of the transmitted light, and discuss its physical significanc…
We propose to implement the Jaynes-Cummings model by coupling a few-micrometer large atomic ensemble to a quantized cavity mode and classical laser fields. A two-photon transition resonantly couples the single-atom ground state |g> to a Rydberg state |e> via a non-resonant intermediate state |i>, but due to the interaction between Rydberg atoms only a single atom can be resonantly excited in the ensemble. This restricts the state space of the ensemble to the collective ground state |G> and the collectively excited state |E> with a single Rydberg excitation distributed evenly on all atoms. The …
We study interactions between polaritons, arising when photons strongly couple to collective excitations in an array of two-level atoms trapped in an optical lattice inside a cavity. We consider two types of interactions between atoms: Dipolar forces and atomic saturability, which ranges from hard-core repulsion to Rydberg blockade. We show that, in spite of the underlying repulsion in the subsystem of atomic excitations, saturability induces a broadband bunching of photons for two-polariton scattering states. We interpret this bunching as a result of interference, and trace it back to the mis…
We report a high-finesse bow-tie cavity designed for atomic physics experiments with Rydberg atom arrays. The cavity has a finesse of $51,000$ and a waist of $7.1$ $μ$m at the cesium D2 line ($852$ nm). With these parameters, the cavity is expected to induce strong coupling between a single atom and a single photon, corresponding to a cooperativity per traveling mode of $35$ at the cavity waist. To trap and image atoms, the cavity setup utilizes two in-vacuum aspheric lenses with numerical aperture ($NA$) of $0.35$ and is capable of housing $NA=0.5$ microscope objectives. In addition, the larg…
Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave to optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric dipole transitions. Here we report on the realization of coherent coupling of a Rydberg transition of ultracold atoms trapped on an integrated superconducting atom chip to the microwave field of an on-chip coplanar waveguid…
A dissipative scheme is proposed to prepare tripartite $W$ state in a Rydberg-atom-cavity system. It is an organic combination of quantum Zeno dynamics, Rydberg antiblockade and atomic spontaneous emission to turn the tripartite $W$ state into the unique steady state of the whole system. The robustness against the loss of cavity and the feasibility of the scheme are demonstrated thoroughly by the current experimental parameters, which leads to a high fidelity above $98\%$.
We describe a novel method for producing Greenberger-Horne-Zeilinger states in cold atoms coupled to a superconducting coplanar cavity. In the proposed scheme, atoms interact between each other by virtual photon exchange via a cavity mode. These interactions cause an asymmetric Rydberg blockade mechanism that suppresses simultaneous excitations into different atomic Rydberg levels, thus forcing all atoms to occupy the same Rydberg state. This mechanism has effect even if the atoms are separated by distances of the order of millimeters. The atomic populations are transferred adiabatically from …
We experimentally characterize the optical nonlinear response of a cold atomic medium placed inside an optical cavity, and excited to Rydberg states. The excitation to S and D Rydberg levels is carried out via a two-photon transition in an EIT (electromagnetically induced transparency) configuration, with a weak (red) probe beam on the lower transition, and a strong (blue) coupling beam on the upper transition. The observed optical nonlinearities induced by S states for the probe beam can be explained using a semi-classical model with van der Waals' interactions. For the D states, it appears n…
We propose an implementation of a universal quantum gate between pairs of spatially separated atoms in a microwave cavity at finite temperature. The gate results from reversible laser excitation of Rydberg states of atoms interacting with each other via exchange of virtual photons through a common cavity mode. Quantum interference of different transition paths between the two-atom ground and double-excited Rydberg states makes both the transition amplitude and resonance largely insensitive to the excitations in the microwave cavity "quantum bus" which can therefore be in any superposition or m…
For neutral atom qubits, the two-qubit gate is typically realized via the Rydberg blockade effect, which hints about the special status of the Rydberg level besides the regular qubit register states. Here, we carry out experimental and theoretical studies to reveal how the ground-Rydberg coherence of the control qubit atom affects the process of two-qubit Controlled-Z ($C_Z$) gate, such as the commonly used ground-Rydberg $π$-gap-$π$ pulse sequence originally proposed in Phys. Rev. Lett. \textbf{85}, 2208 (2000). We measure the decoherence of the control qubit atom after the $π$-gap-$π$ pulses…
We investigate the coherent manipulation of interacting Rydberg atoms placed inside a high-finesse optical cavity for the deterministic preparation of strongly coupled light-matter systems. We consider a four-level diamond scheme with one common Rydberg level for N interacting atoms. One side of the diamond is used to excite the atoms into a collective `superatom' Rydberg state using either π-pulses or stimulated Raman adiabatic passage (STIRAP) pulses. The upper transition on the other side of the diamond is used to transfer the collective state to one that is coupled to a field mode of an op…
We study the atom-photon quantum interface with intracavity Rydberg-blocked atomic ensemble where the ground-Rydberg transition is realized by two-photon transition. Via theoretical analysis, we report our recent findings of the Jaynes-Cummings model on optical domain and robust atom-photon quantum gate enabled by this platform. The requirement on the implementation is mild which includes an optical cavity of moderately high finesse, typical alkali atoms such as Rb or Cs and the condition that cold atomic ensemble is well within the Rydberg blockade radius. The analysis focuses on the atomic e…
Rydberg atoms traversing a micromaser cavity one after the other can emerge in correlated states, and according to Copenhagen quantum mechanics this may lead to a violation of Bell's inequality, that is, to a Bell sum S>2. S is here calculated in various ideal physical situations including those with (1) different initial states of the atoms, (2) different free adjustable parameters, being either the phase or the turning angle of a classical radiation field put behind the cavity, and (3) either equal or different Rabi angles for successive atoms. The experiments are crucial for a realist inter…
Recently, the creation of photonic Landau levels in a twisted cavity has been demonstrated in Nature \textbf{534}, 671 (2016). Here we propose a scheme to adiabatically transfer flux quanta in multiples of $3\hbar$ simultaneously to all cavity photons by coupling the photons through flux-threaded cones present in such cavity setup. The flux transfer is achieved using external light fields with orbital angular momentum and a near-resonant dense atomic medium as mediator. Furthermore, coupling the cavity fields to a Rydberg state in a configuration supporting electromagnetically induced transpar…
We report results of a ground-state entanglement protocol for a pair of Cs atoms separated by 6~$μ$m, combining the Rydberg blockade mechanism with a two-photon Raman transitions to prepare the $\vertΨ^+\rangle=(\vert 10\rangle+\vert 01\rangle)/\sqrt{2}$ Bell state with a loss-corrected fidelity of 0.81(5), equal to the best demonstrated fidelity for atoms trapped in optical tweezers but without the requirement for dynamically adjustable interatomic spacing. Qubit state coherence is also critical for quantum information applications, and we characterise both ground-state and ground-Rydberg dep…
We present an entanglement scheme for Rydberg atoms using the van der Waals interaction phase induced by Ramsey-type pulsed interactions. This scheme realizes not only controlled phase operations between atoms at a distance larger than Rydberg blockade distance, but also various counter-intuitive entanglement examples, including two-atom entanglement in the presence of a closer third atom and $W$-state generation for partially-blockaded three atoms. Experimental realization is conducted with single rubidium atoms loaded in an array of optical tweezer dipole traps, to demonstrate the proposed e…
Quantum spin liquids are exotic phases of matter that are prevented from being frozen even at zero temperature, and appear disordered by local probes that monitor the subsystems. Driven by quantum fluctuations, topological spin liquids are manifested by their long-range entanglement, and are characterized by quasiparticles with fractional statistics. Here, we make contact of a 2D Rydberg ice to a QED vacuum of an ultra-high-finesse optical cavity, and dynamically promote the frustrated background field of the spin ice to a $\mathbb{Z}_2$ spin liquid. We characterize the deconfined nature of th…
We investigate the dynamical Casimir effect and its detection with Rydberg atoms. The photons are created in a resonant cavity with a plasma mirror of a semiconductor slab which is irradiated by periodic laser pulses. The canonical Hamiltonian is derived for the creation and annihilation operators showing the explicit time-variation in the couplings, which originates from the external configuration such as a nonstationary plasma mirror. The number of created photons is evaluated as squeezing from the Heisenberg equations with the Hamiltonian. Then, the detection of the photons as the atomic ex…
We carry out a study on thermodynamics properties as entropy and heat $J_{Q}$ and work $J_{W}$ fluxes involved in a Ramsey zone, i.e., a mode field inside a low quality factor cavity that behaves classically and promotes rotations on atomic states. Focusing on the atomic dynamic only, here we show that $J_{W}$ predominates when the atomic state evolves maintaining its maximum purity, as computed by von Neumann entropy, in which case the rotation is successfully applied. On the other hand, $J_{Q}$ is the quantity that stands out when the atomic state ceases to be pure due to its entanglement wi…
We study the two-dimensional Rydberg atom array in an optical cavity with help of the meanfield theory and the large-scale quantum Monte Carlo simulations. The strong dipole-dipole interactions between Rydberg atoms can make the system exhibit the crystal structure, and the coupling between two-level atom and cavity photon mode can result in the formation of the polariton. The interplay between them provides a rich quantum phase diagram including the Mott, solid-1/2, superradiant and superradiant solid phases. As the two-order co-existed phase, the superradiant solid phase breaks both translat…
We observe and measure dispersive optical non-linearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical non-linearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
We propose a realizable experimental scheme to prepare a superposition of the vacuum and one-photon states using a typical cavity QED-setup. This is different from previous schemes, where the superposition state of the field is generated by resonant atom-field interaction and the cavity is initially empty. Here, we consider only dispersive atom-field interaction and the initial state of the cavity field is coherent. Then, we determine the parameters to prepare the desired state via atomic postselection. We also include the effect of cavity losses and detection imperfections in our analysis, ag…
The millimeter wave (mm-wave) frequency band provides exciting prospects for quantum science and devices, since many high-fidelity quantum emitters, including Rydberg atoms, molecules and silicon vacancies, exhibit resonances near 100 GHz. High-Q resonators at these frequencies would give access to strong interactions between emitters and single photons, leading to rich and unexplored quantum phenomena at temperatures above 1K. We report a 3D mm-wave cavity with a measured single-photon internal quality factor of $3 \times 10^{7}$ and mode volume of $0.14 \times λ^3$ at $98.2$ GHz, sufficient …
We study the dynamics of a system composed of two coupled cavities, each containing a single Rydberg atom. The interplay between Rydberg-Rydberg interaction and photon hopping enables the transition of the atoms from the collective ground state to the double Rydberg excitation state by individually interacting with the hybrid cavity modes and suppressing the up conversion process between them. The atomic transition is accompanied by the two-photon absorption and emission of the hybrid modes. Since the energy level structure of the atom-cavity system is photon number dependent, there is only a …
We present a versatile laser system which provides more than 1.5W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial Titanium-Sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we…
We adapt a typical Ramsey interferometer by inserting a linear accelerator capable of accelerating an atom inside a single-mode cavity. We demonstrate that this simple scheme allows us to estimate the effects of acceleration radiation via interferometric visibility. By using a Rydberg-like atom, our results suggest that, for the transition regime of the order of GHz and interaction time of 1 ns, acceleration radiation effects can be observable for accelerations as low as $10^{17}$ m/s$^2$.
A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth $nonclassical$ light. The cavity nonlinearity induced by the Rydberg medium strongly modifies the superradiance threshold, and leads to a Mollo…
Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we veri…
Inspired by a recent work [Reiter, Reeb, and Sørensen, Phys. Rev. Lett. {\bf117}, 040501 (2016)], we present a simplified proposal for dissipatively preparing a Greenberger-Horne-Zeilinger (GHZ) state of three Rydberg atoms in a cavity. The $Z$ pumping is implemented under the action of the spontaneous emission of $Λ$-type atoms and the quantum Zeno dynamics induced by strong continuous coupling. In the meantime, a dissipative Rydberg pumping breaks up the stability of the state $|{\rm GHZ}_+\rangle$ in the process of $Z$ pumping, making $|{\rm GHZ}_-\rangle$ be the unique steady state of syst…
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.
A novel scheme is proposed for dissipative generation of maximally entanglement between two Rydberg atoms in the context of cavity QED. The spontaneous emission of atoms combined with quantum Zeno dynamics and Rydberg antiblockade guarantees a unique steady solution of the master equation of system, which just corresponds to the antisymmetric Bell state $|S\rangle$. The convergence rate is accelerated by the ground-state blockade mechanism of Rydberg atoms. Meanwhile the effect of cavity decay is suppressed by the Zeno requirement, leading to a steady-state fidelity about $90\%$ as the single-…
