We investigate the collective aspects of Rydberg excitation in ultracold mesoscopic systems. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitation are the many-body Rabi oscillations, spatial correlations between atoms as well as the fluctuations of the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schrëdinger equation.
We demonstrate Rabi flopping of small numbers of $\rm{^{87}Rb}$ atoms between ground and Rydberg states with $n\le 43$. Coherent population oscillations are observed for single atom flopping, while the presence of two or more atoms decoheres the oscillations. We show that these observations are consistent with van der Waals interactions of Rydberg atoms.
With a resonant amplitude-modulation field on two Rydberg atoms, we propose a Rydberg antiblockade (RAB) regime, where the Rabi oscillation between collective ground and excited states is induced. A controlled-Z gate can be yielded through a Rabi cycle. Further, several common issues of the RAB gates are solved by modifying the parameter relation. The gate fidelity and the gate robustness against the control error are enhanced with a shaped pulse. The requirement of control precision of the Rydberg-Rydberg interaction strength is relaxed. In addition, the atomic excitation is restrained and th…
The dynamics of the Jaynes-Cummings Hamiltonian is studied in the semiclassical limit by reducing it to quantum normal form and deriving the phase space dynamics of classically smooth observables. The resulting systematic semiclassical approximation is used to analyze the Rabi oscillations of a photon wave packet revealing subtle consequences of the uncertainty principle.
The dipole blockade of multiple Rydberg excitations in mesoscopic atomic ensembles allows the implementation of various quantum information tasks using collective states of cold, trapped atoms. Precise coherent manipulations of the collective ground and single Rydberg excitation states of an atomic ensemble requires the knowledge of the number of atoms with small uncertainty. We present an efficient method to acquire such information by interrogating the atomic ensemble with resonant pulses while monitoring the resulting Rydberg excitations. We show that after several such steps accompanied by…
We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-err…
We demonstrate theoretically a parallelized C-NOT gate which allows to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond timescale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering Electromagnetically Induced Transparency (EIT). By this we can robustly implement a conditional transfer of all ensemble atoms among two logical states, depending on the state of the control atom. We outline a many body interferometer which allows a comparison of two many-body quantum states by perf…
We report on the observation of Rabi oscillations to a Rydberg state on a timescale below one nanosecond in thermal rubidium vapor. We use a bandwidth-limited pulsed excitation and observe up to 6 full Rabi cycles within a pulse duration of ~ 4 ns. We find good agreement between the experiment and numerical simulations based on a surprisingly simple model. This result shows that fully coherent dynamics with Rydberg states can be achieved even in thermal atomic vapor thus suggesting small vapor cells as a platform for room temperature quantum devices. Furthermore the result implies that previou…
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of `cat' states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their qu…
Motivated by experimental advances [e.g. A. Ga{ë}tan {\it et.al.} Nat. Phys. 5 115 (2009)] that the collective excitation of two Rydberg atoms was observed, we provide an elaborate theoretical study for the dynamical behavior of two-atom Rabi oscillations. In the large-intermediate-detuning case, the two-photon Rabi oscillation is found to be significantly affected by the strength of the interatomic van der Waals interaction. With a careful comparison of the exact numbers and values of the oscillation frequency, we propose a new way to determine the strength of excitation blockade, well agreei…
We use coherent excitation of 3-16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected $\sqrt{N}$ Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with essentially perfect blockade. We then use collective Rabi $π$ pulses to produce ${\cal N}=1,2$ atom number Fock states with fidelities of 62% and 48% respectively. The ${\cal N}=2$ Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuatio…
We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of Rydberg blockade, where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interac…
We propose a mechanism of unconventional Rydberg pumping (URP) via simultaneously driving each Rydberg atom by two classical fields with different strengths of Rabi frequencies. This mechanism differs from the general Rydberg blockade or Rydberg antiblockade since it is closely related to the ground states of atoms, i.e. two atoms in the same ground state are stable while two atoms in different ground states are resonantly excited. Furthermore, we find the URP can be employed to simplify some special quantum information processing tasks, such as implementation of a three-qubit controlled phase…
We suggest a novel way to use strong Rydberg dipole-dipole interactions in order to induce non-trivial conditional dynamics in individual-atom systems and mesoscopic ensembles. Contrary to previous works, we suggest to excite atoms into different Rydberg states, which results in a potentially richer dynamical behaviour. Specifically, we investigate systems of individual hydrogen-like atoms or mesoscopic ensembles excited into high-lying hydrogen-like s, p or d states and show how to perform three-qubit conditional dynamics on the information they contain through a proper use of dipole-dipole i…
We propose an efficient method to filter out single atoms from trapped ensembles with unknown number of atoms. The method employs stimulated adiabatic passage to reversibly transfer a single atom to the Rydberg state which blocks subsequent Rydberg excitation of all the other atoms within the ensemble. This triggers the excitation of Rydberg blockaded atoms to short lived intermediate states and their subsequent decay to untrapped states. Using an auxiliary microwave field to carefully engineer the dissipation, we obtain a nearly deterministic single-atom source. Our method is applicable to sm…
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…
We study the population dynamics in a two-atom setup in which each atom is driven independently by different light fields, but coupling the same Rydberg state. In particular, we look at how an offset in the Rabi frequencies between two atoms influences the dynamics. We find novel features such as amplifying the Rabi frequency of one atom, together with strong Rydberg-Rydberg interactions freezes the dynamics in the second atom. We characterize the Rydberg-biased freezing phenomenon in detail, with effective Hamiltonians obtained for various limits of the system parameters. In the absence of Ra…
An array of single Rydberg atoms driven by a frequency modulated light field is studied. The periodic modulation effectively modifies the Rabi coupling, leading to unprecedented dynamics in the presence of Rydberg-Rydberg interactions. They include state dependent population trapping, the Rydberg blockade for small and anti-blockades at large interaction strengths. Interestingly, the Schrieffer-wolf transformation reveals a fundamental process in Rydberg gases, correlated Rabi oscillations, arising from the long-range interactions, provides an alternative depiction for Rydberg blockade and it …
Universidade Federal do Rio Grande do Norte（北里奥格兰德联邦大学）；Stockholm University（斯德哥尔摩大学）
We simulate the dissipative dynamics of a mesoscopic system of long-range interacting particles which can be mapped into non-Hermitian spin models with a $\mathcal{PT}$ symmetry. We find rich $\mathcal{PT}$-phase diagrams with $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken phases. The dynamical regimes can be further enriched by modulating tunable parameters of the system. We outline how the $\mathcal{PT}$ symmetries of such systems may be probed by studying their dynamics. We note that systems of Rydberg atoms and systems of Rydberg ions with strong dipolar interactions are particularly w…
We study experimentally various physical limitations and technical imperfections that lead to damping and finite contrast of optically-driven Rabi oscillations between ground and Rydberg states of a single atom. Finite contrast is due to preparation and detection errors and we show how to model and measure them accurately. Part of these errors originates from the finite lifetime of Rydberg states and we observe its $n^3$-scaling with the principal quantum number $n$. To explain the damping of Rabi oscillations, we use simple numerical models, taking into account independently measured experime…
Blockade effects on the single quantum level are at the heart of quantum devices like single-electron transistors. The blockade mechanisms are based on strong interactions like the Coulomb interaction in case of single electrons. Neutral atoms excited into a Rydberg state experience abnormally strong interactions that lead to the corresponding blockade effect for Rydberg atoms. In this paper we report on our measurements of a strong van der Waals blockade, showing that only one out of several thousand atoms within a blockade volume can be excited. In addition, our experimental results demonstr…
The collective effect of large amounts of atoms exhibit an enhanced interaction between light and atoms. This holds great interest in quantum optics, and quantum information. When a collective excited state of a group of atoms during Rabi oscillation is varying, the oscillation exhibits rich dynamics. Here, we experimentally observe a size-reduction effect of the Rydberg collective state during Rabi oscillation in cold atomic dilute gases. The Rydberg collective state was first created by the Rydberg quantum memory, and we observed a decreased oscillation frequency effect by measuring the time…
We present schemes for geometric phase compensation in adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using the…
Giant impurity excitations with large binding energies are powerful probes for exploring new regimes of far out of equilibrium dynamics in few- and many-body quantum systems, as well as for in-situ observations of correlations. Motivated by recent experimental progress in spectroscopic studies of Rydberg excitations in ensembles of ultracold atoms, we develop a new theoretical approach for describing multiscale dynamics of Rydberg excitations in quantum Bose gases. We find that the crossover from few- to many-body dynamics manifests in a dramatic change in spectral profile from resolved molecu…
A quantum-feedback-based scheme is proposed for generating multipartite entanglements of Rydberg atoms in a dissipative optical cavity. The Rydberg blockade mechanism efficiently prevents double excitations of the system, which is further exploited to speed up the stabilization of an entangled state with a single Rydberg state excitation. The corresponding feedback operations are greatly simplified, since only one regular atom needs to be controlled during the whole process, irrespective of the number of particles. The form of entangled state is also adjustable via regulating the Rabi frequenc…
Numerically optimized amplitude-robust controlled-Z gate for ultracold neutral atoms with individual addressing capability
Rzhanov Institute of Semiconductor Physics SB RAS（拉扎诺夫半导体物理研究所西伯利亚分院）；Novosibirsk State University（新西伯利亚国立大学）；Institute of Laser Physics SB RAS（激光物理研究所西伯利亚分院）；Novosibirsk State Technical University（新西伯利亚国立技术大学）
We present the coherent excitation of a single Rubidium atom to the Rydberg state (58d3/2) using a two-photon transition. The experimental setup is described in detail, as well as experimental techniques and procedures. The coherence of the excitation is revealed by observing Rabi oscillations between ground and Rydberg states of the atom. We analyze the observed oscillations in detail and compare them to numerical simulations which include imperfections of our experimental system. Strategies for future improvements on the coherent manipulation of a single atom in our settings are given.
We propose a scheme for preparation of large-scale entangled $GHZ$ states and $W$ states with neutral Rydberg atoms. The scheme mainly depends on Rydberg antiblockade effect, i.e., as the Rydberg-Rydberg-interaction (RRI) strength and the detuning between the atom transition frequency and the classical laser frequency satisfies some certain conditions, the effective Rabi oscillation between the two ground states and the two excitation Rydberg states would be generated. The prominent advantage is that both two-multiparticle $GHZ$ states and two-multiparticle $W$ states can be fused in this mode…
We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $Ω$. In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $Ω^4$, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pul…
High-fidelity entangling quantum gates based on Rydberg interactions are required for scalable quantum computing with neutral atoms. Their realization, however, meets a major stumbling block -- the motion-induced dephasing of the transition between the ground and Rydberg states. By using quantum interference between different detuned Rabi oscillations, we propose a practical scheme to realize a class of accurate entangling Rydberg quantum gates subject to a minimal dephasing error. We show two types of such gates, $U_{1}$ and $U_{2}$, in the form of $\text{diag}\{1, e^{iα}, e^{iγ}, e^{iβ}\}$, …
Controlling strongly interacting many-body systems enables the creation of tailored quantum matter, with properties transcending those based solely on single particle physics. Atomic ensembles which are optically driven to a Rydberg state provide many examples of this, such as atom-atom entanglement, many-body Rabi oscillations, strong photon-photon interaction and spatial pair correlations. In its most basic form, Rydberg quantum matter consists of an isolated ensemble of strongly interacting atoms spatially confined to the blockade volume - a so-called superatom. Here we demonstrate the cont…
We realize a coherent transfer between a laser-accessible low-angular-momentum Rydberg state and the circular Rydberg level with maximal angular momentum. This transfer is induced by a radiofrequency field with a high-purity $σ^+$ polarization tuned at resonance on Stark transitions inside the hydrogenic Rydberg manifold. We observe over a few microseconds more than twenty coherent Rabi oscillations between the initial Rydberg state and the circular Rydberg level. We characterize in details these complex oscillations involving many Rydberg levels and find them to be in perfect agreement with a…
We observe the nonlinearity of the Jaynes-Cummings (JC) ladder in the Autler-Townes spectroscopy of the hyperfine ground states for a Rydberg-dressed two-atom system. Here the role of the two-level system in the JC model is played by the presence or absence of a collective Rydberg excitation, and the bosonic mode manifests as the number $n$ of single atom spin flips, symmetrically distributed between the atoms. We measure the normal-mode splitting and $\sqrt{n}$ nonlinearity as a function of detuning and Rabi frequency, thereby experimentally establishing the isomorphism with the JC model.
Entangled states are crucial for modern quantum enabled technology which makes their creation key for future developments. In this paper, a robust quantum control methodology is presented to create entangled states of two typical classes, the W and the Greenberger-Horne-Zeilinger (GHZ). It was developed from the analysis of a chain of alkali atoms $^{87}Rb $ interaction with laser pulses, which lead to the two-photon transitions from the ground to the Rydberg states with a predetermined magnetic quantum number. The methodology is based on the mechanism of two-photon adiabatic passage using ove…
We propose a scheme for rapid generation of high fidelity steady state entanglement between a pair of atoms. A two-photon excitation process towards long-lived Rydberg states with finite pairwise interaction, a dark state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly…
Rydberg arrays merge the collective behavior of ordered atomic arrays with the controllability and optical nonlinearities of Rydberg systems, resulting in a powerful platform for realizing photonic many-body physics. As an application of this platform, we propose a protocol for quantum non-demolition (QND) photon counting. Our protocol involves photon storage in the Rydberg array, an observation phase consisting of a series of Rabi flops to a Rydberg state and measurements, and retrieval of the stored photons. The Rabi frequency experiences a $\sqrt{n}$ collective enhancement, where $n$ is the…
Compared with the idea of universal quantum computation, a direct synthesis of a multiqubit logic gate can greatly improve the efficiency of quantum information processing tasks. Here we propose an efficient scheme to implement a three-qubit controlled-not (Toffoli) gate of neutral atoms based on unconventional Rydberg pumping. By adjusting the strengths of Rabi frequencies of driving fields, the Toffoli gate can be achieved within one step, which is also insensitive to the fluctuation of the Rydberg-Rydberg interaction. Considering different atom alignments, we can obtain a high-fidelity Toff…
A two-level quantum system coherently driven by a resonant electromagnetic field oscillates sinusoidally between the two levels at frequency $Ω$ which is proportional to the field amplitude [1]. This phenomenon, known as the Rabi oscillation, has been at the heart of atomic, molecular and optical physics since the seminal work of its namesake and coauthors [2]. Notably, Rabi oscillations in isolated single atoms or dilute gases form the basis for metrological applications such as atomic clocks and precision measurements of physical constants [3]. Both inhomogeneous distribution of coupling str…
We investigate the possibilities for a deterministic conversion between two important types of maximally entangled multiqubit states, namely, $W$ and Greenberger-Horne-Zeilinger (GHZ) states, in the Rydberg-blockade regime of a neutral-atom system where each atom is subject to four external laser pulses. Such interconversions between $W$ states and their GHZ counterparts have quite recently been addressed using the method of shortcuts to adiabaticity, more precisely techniques based on Lewis-Riesenfeld invariants [R.-H. Zheng {\em et al.}, Phys. Rev. A {\bf 101}, 012345 (2020)]. Motivated in p…
The recent observation of high-lying Rydberg states of excitons in semiconductors with relatively high binding energy motivates exploring their applications in quantum nonlinear optics and quantum information processing. Here, we study Rydberg excitation dynamics of a mesoscopic array of excitons to demonstrate its application in simulation of quantum many-body dynamics. We show that the $\mathbb{Z}_2$-ordered phase can be reached using physical parameters available for cuprous oxide (Cu$_2$O) by optimizing driving laser parameters such as duration, intensity, and frequency. In an example, we …
The coherent control of mesoscopic ensembles of atoms and Rydberg atom blockade are the basis for proposed quantum devices such as integrable gates and single photon sources. So far, experimental progress has been limited to complex experimental setups that use ultracold atoms. Here, we show that coherence times of ~100ns are achievable with coherent Rydberg atom spectroscopy in um sized thermal vapor cells. We investigated states with principle quantum numbers between 30 and 50. Our results demonstrate that microcells with a size on the order of the blockade radius, ~2um, at temperatures of 1…
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…
We analyze excitation of two ground state atoms to a double Rydberg state by a two-photon chirped optical pulse in the regime of adiabatic rapid passage. For intermediate Rydberg-Rydberg interaction strengths, relevant for atoms separated by $\sim$ten $μ$m, adiabatic excitation can be achieved at experimentally feasible Rabi frequencies and chirp rates of the pulses, resulting in high transfer efficiencies. We also study the adiabatic transfer between ground and Rydberg states as a means to realize a controlled phase gate between atomic qubits.
Assembled arrays of individual atoms with Rydberg-mediated interactions provide a powerful platform for the simulation of many-body spin Hamiltonians as well as the implementation of universal gate-based quantum information processing. We demonstrate the first realization of Rydberg excitations and controlled interactions in microlens-generated multisite trap arrays of reconfigurable geometry. We utilize atom-by-atom assembly for the deterministic preparation of pre-defined 2D structures of rubidium Rydberg atoms with exactly known mutual separations and selectable interaction strength. By ada…
We present evidence for Rydberg-Rydberg interaction in a gas of rubidium atoms above room temperature. Rabi oscillations on the nanosecond timescale to different Rydberg states are investigated in a vapor cell experiment. Analyzing the atomic time evolution and comparing to a dephasing model we find a scaling with the Rydberg quantum number n that is consistent with van der Waals interaction. Our results show that the interaction strength can be larger than the kinetic energy scale (Doppler width) which is the requirement for realization of thermal quantum devices in the GHz regime.
We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting ``dipole blockade'' can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as non-classical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.
Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by a Rydberg interaction of similar magnitude to the Rydberg Rabi frequency, we study a controlled-phase gate with an arbitrary phase and extend it to the controlled-NOT gate. The gates need only three steps for coupling one Rydberg state, depend on easily accessible van der Waals interaction that naturally arises between distant atoms, and have no rotat…
We present experiments on two-photon excitation of ${\rm ^{87}}$Rb atoms to Rydberg states. For this purpose, two continuous-wave (cw)-laser systems for both 780 nm and 480 nm have been set up. These systems are optimized to a small linewidth (well below 1 MHz) to get both an efficient excitation process and good spectroscopic resolution. To test the performance of our laser system, we investigated the Stark splitting of Rydberg states. For n=40 we were able to see the hyperfine levels splitting in the electrical field for different finestructure states. To show the ability of spatially select…
We study theoretically and experimentally the competing blockade and anti-blockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system's behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qu…
The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1-5 atoms when they are detected by the selective field ionization method. We investigated the spectra of the t…
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…
Robust controlled-Z gate for Rydberg atoms based on level-crossing-free echoing rapid adiabatic passage
College of Physics and Electronic Engineering, Shanxi University（山西大学物理电子工程学院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
