Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms

Lying ≥4 eV above the ground state, Rydberg states are not populated thermally, except at very high temperatures. Accordingly, it is natural to assume that thermal effects are negligible in dealing with Rydberg atoms. However, Rydberg atoms are strongly affected by black body radiation, even at room temperature. The dramatic effect of thermal radiation is due to two facts. First, the energy spacings Δ W between Rydberg levels are small, so that Δ W kT at 300 K. Second, the dipole matrix elements of transitions between Rydberg states are large, providing excellent coupling of the atoms to the thermal radiation. The result of the strong coupling between Rydberg atoms and the thermal radiation is that population initially put into one state, by laser excitation for example, rapidly diffuses to other energetically nearby states by black body radiation induced dipole transitions. Both the redistribution of population and the implicit increase in the radiative decay rates are readily observed. Although the above mentioned effects on level populations are the most obvious effects, the fact that a Rydberg atom is immersed in the thermal radiation field increases its energy by a small amount, 2 kHz at 300 K. While the radiation intensity is vastly different in the two cases, this effect is the same as the ponderomotive shift of the ionization limit in high intensity laser experiments.

The motion-induced dephasing is a severe problem that limits the accuracy of a quantum control process by using external laser fields in neutral Rydberg atoms. This dephasing is a major issue that limits the realizable fidelity of a quantum entangling gate with neutral atoms when there is a {\it gap} time for the Rydberg atom to drift freely. We find that such a dephasing can be largely suppressed by using a transition in a `V'-type dual-rail configuration. The left~(right) arm of this `V' represents a transition to a Rydberg state $|r_{1(2)}\rangle$ with a Rabi frequency $\Omega e^{ikz}~(\Omega e^{-ikz})$, where $z$ is frozen without atomic drift, but changes linearly in each experimental cycle. Such a configuration is equivalent to a transition between the ground state and a hybrid and time-dependent Rydberg state with a Rabi frequency $\sqrt2\Omega$, such that there is no phase error whenever the state returns to the ground state. We study two applications of this method. First, it is possible to faithfully transfer the atomic state between a hyperfine ground state $|1\rangle$ and Rydberg states $|r_{1(2)}\rangle$ with no {\it gap} time between the excitation and deexcitation. Second, by adding infrared laser fields to induce transition between $|r_{1(2)}\rangle$ and a nearby Rydberg state $|r_3\rangle$ via a largely detuned low-lying intermediate state in the {\it gap} time, the atom can keep its internal state in the Rydberg level as well as adjust the population branching in $|r_{1(2)}\rangle$ during the {\it gap} time. This allows an almost perfect Rydberg deexcitation after the {\it gap} time, making it possible to recover a high fidelity in the Rydberg blockade gate. The theory paves the way for high-fidelity quantum control over neutral Rydberg atoms without cooling qubits to the motional ground states in optical traps.

The nonadiabatic geometric quantum computation is promising as it is robust against certain types of local noises. However, its experimental implementation is challenging due to the need of complex control on multi-level and/or multiple quantum systems. Here, we propose to implement it on a two-dimensional square superconducting qubit lattice. In the construction of our geometric quantum gates, we only use the simplest and experimentally accessible control over the qubit states of the involved quantum systems, without introducing any auxiliary state. Specifically, our scheme is achieved by parametrically tunable all-resonant interaction, which leads to high-fidelity quantum gates. Meanwhile, this simple implementation can be conveniently generalized to a composite scenario, which can further suppress the systematic error during the gate operations. In addition, universal nonadiabatic geometric quantum gates in decoherence-free subspace can also be realized based on the tunable coupling between only two transmon qubits, without consulting to multiple qubits and only using two physical qubits to encode a logical qubit. Therefore, our proposal provides a promising way of high-fidelity geometric manipulation for robust solid-state quantum computation.

We report on the experimental characterization of various types of spin-exchange interactions between two individual atoms, where pseudospin degrees of freedom are encoded in different Rydberg states. For the case of the direct dipole-dipole interaction between states of opposite parity, such as between $|nS\ensuremath{\rangle}$ and $|nP\ensuremath{\rangle}$, we investigate the effects of positional disorder arising from the residual atomic motion on the coherence of spin-exchange oscillations. We then characterize an indirect dipolar spin exchange, i.e., the off-diagonal part of the van der Waals effective Hamiltonian that couples the states $|nS\ensuremath{\rangle}$ and $|(n+1)S\ensuremath{\rangle}$. Finally, we report on the observation of a new type of dipolar coupling, made resonant using addressable light shifts and involving four different Rydberg levels: this exchange process is akin to electrically induced F\"orster resonance, but featuring local control. It exhibits an angular dependence distinct from the usual $1\ensuremath{-}3{cos}^{2}(\ensuremath{\theta})$ form of the resonant dipolar spin-exchange.

Cold Rydberg atoms, known for their long lifetimes and strong dipole-dipole interactions that lead to the Rydberg blockade phenomenon, are among the most promising platforms for quantum simulations, quantum computation and quantum networks. However, a major limitation to the performance of Rydberg atom-based platforms is dephasing, which can be caused by atomic motion within the trap. Here, we propose a trap for 87Rb cold atoms that confines both the electronic ground state and a Rydberg state, engineered to minimize the differential light shifts between the two states. This is achieved by combining a fictitious magnetic field induced by optical nanofiber (ONF) guided light and an external bias magnetic field. We calculate trap potentials for the cases of one- and two-guided modes with quasi-linear and quasi-circular polarizations, and calculate trap depths and trap frequencies for different values of laser power and bias fields. Moreover, we discuss the impact of the quadrupole polarisability of the Rydberg atoms on the trap potential and demonstrate how the size of a Rydberg atom influences the ponderomotive potential generated by the nanofiber-guided light field. This work expands on the idea of light-induced fictitious magnetic field traps and presents a practical approach for creating quantum networks using Rydberg atoms integrated with ONFs to generate 1D atom arrays.

A Rydberg atom is an atom excited to a high energy level, and there is a strong dipole-dipole interaction between nearby Rydberg atoms. While there has been much interest in closed systems of Rydberg atoms, less is known about open systems of Rydberg atoms with spontaneous emission. This thesis explores the latter. We consider a lattice of atoms, laser-excited from the ground state to a Rydberg state and spontaneously decaying back to the ground state. Using mean-field theory, we study the how the steady-state Rydberg population varies across the lattice. There are three phases: uniform, antiferromagnetic, and oscillatory. Then we consider the dynamics of the quantum model when mean-field theory predicts bistability. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden. Finally, we let each atom be laser-excited to a short-lived excited state in addition to a Rydberg state. This three-level configuration leads to rich spatiotemporal dynamics that are visible in the fluorescence from the short-lived excited state. The atoms develop strong spatial correlations that change on a long time scale.

The difference in the static electric dipole polarizabilities of the and Rydberg levels in helium has been eliminated by dressing the atom with a microwave field near resonant with the single-photon transition. For an amplitude dressing field, detuned by from the zero-field transition frequency, the dc Stark shift of the two-photon transition between these states remained within for electric fields up to . This transition was probed by single-color two-photon microwave spectroscopy, and by two-color two-photon spectroscopy with one strong additional dressing field and a weak probe field. For all measurements, the transition frequencies and Stark shifts were compared, and found to be in excellent quantitative agreement with the results of Floquet calculations of the energy-level structure of the Rydberg states in the presence of the dressing fields and applied dc electric fields. The two-color microwave dressing scheme demonstrated, with one field applied to null the differential polarizability of the Rydberg–Rydberg transition, and the second exploited to allow the two-photon transition to be employed to achieve tunable absorption of single-photons from a weak probe field, will facilitate improved coherence times and tunable single-photon absorption in hybrid cavity QED experiments with Rydberg atoms and superconducting microwave circuits.

We propose an approach to detect individual Rydberg molecules, where each molecule consists of two atoms lying in different Rydberg states. The scheme exploits the different movements of atoms and molecules in the presence of external forces to differentiate atoms and molecules. The forces acting on the two atoms in the molecule are different. We consider the most ideal situation, that is, the external force is exerted only on one of the two Rydberg atoms in the molecule. The movement of Rydberg atoms that are not affected by the external force depends on whether they are bound to the Rydberg atoms affected by the force. Therefore, bound Rydberg atoms can be distinguished from free Rydberg atoms. By non-destructively resolving the locations of Rydberg atoms through detecting the absorption events with the probe field or the fluorescence signal, the scheme can be utilized to detect the positions of Rydberg molecules, and also the bond force in the Rydberg molecule.

Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e., simultaneous excitation of more than one Rydberg atom, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Rydberg atoms interacting via dipole-dipole exchange interactions. We study typical situations in current Rydberg atom experiments, where different types of dipole-dipole interactions can be achieved by varying Rydberg state couplings. An effective Hamiltonian governing underlying antiblockade dynamics is derived. We illustrate that geometric gates can be realized with the Rydberg antiblockade which is robust against the decay of Rydberg states. Our study may stimulate new experimental and theoretical exploration of quantum optics and strongly interacting many-body dynamics with Rydberg antiblockade driven by dipole-dipole interactions.

We present single-photon spectroscopy in molecular hydrogen starting from the metastable c3Piu- state to a number of triplet nd-Rydberg states (v = 0 - 4, n = 12 - 20). Using fast beam spectroscopy both the autoionization channel and the predissociation channel are quantified, field free, as well as with small electric fields. Coupling with the i3Pig state is assumed to be responsible for field-free predissociation of the v = 0 Rydberg levels. The stronger observed predissociation channel of the v = 1 Rydberg levels is due to the nonadiabatic interaction with the h3Sigmag+ state in combination with l mixing due to an external electric field. No direct evidence is found for possible electric field induced predissociation of the gerade Rydberg states by low lying ungerade states. The competition between autoionization and predissociation is discussed in terms of possible consequences for dissociative recombination involving low energy electron collisions with the H2+ molecular ion.

Vibrationally resolved band profiles for autoionisation of NO (c 3Π) nℓλ ( vR=0) Rydberg states into NO + A 1Π ( vi=0, 1, 2) vibronic levels

We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The resulting gate can be implemented with cavities of moderate finesse which allows for highly efficient processing of quantum information encoded in photons. As a particular example of this, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles.

We present experimental results on the influence of magnetic fields and laser polarization on electromagnetically induced transparency (EIT) using Rydberg levels of ^{87}87Rb atoms. The measurements are performed in a room temperature vapor cell with two counter-propagating laser beams at 480 m and 780 m in a ladder-type energy level scheme. We measure the EIT spectrum of a range of ns_{1/2}ns1/2 Rydberg states for n=19-27n=19−27, where the hyperfine structure can still be resolved. Our measurements span the range of magnetic fields from the low field linear Zeeman regime to the high field Paschen-Back regimes. The observed spectra are very sensitive to small changes in magnetic fields and the polarization of the laser beams. We model our observations using optical Bloch equations that take into account the full multi-level structure of the atomic states involved and the decoupling of the electronic JJ and nuclear II angular momenta in the Breit-Rabi regime. The numerical model yields excellent agreement with the observations. In addition to EIT related experiments, our results are relevant for experiments involving coherent excitation to Rydberg levels in the presence of magnetic fields.

Schemes for creation of N particle entangled Greenberger-Horne-Zeilinger\n(GHZ) states are important for understanding multi-particle non-classical\ncorrelations. Here, a theoretical scheme for creation of a multi-particle GHZ\nstate implemented on a target ensemble of N, $\\Lambda$ three-level Rydberg\natoms and a single Rydberg atom as a control using Stimulated Raman Adiabatic\nPassage (STIRAP) is presented. We work in the Rydberg blockade regime for the\nensemble atoms induced due to excitation of the control atom to a high lying\nRydberg level. It is shown that using STIRAP, atoms from one ground state of\nthe ensemble can be adiabatically transferred to the other ground state,\ndepending on the state of the control atom with high fidelity. Measurement of\nthe control atom in a specific basis after this conditional transfer\nfacilitates one-step creation of a N particle GHZ state. A thorough analysis of\nadiabatic conditions for this scheme and the influence of radiative decay from\nthe excited Rydberg levels is presented. We show that this scheme is immune to\nthe decay rate of the excited level in ensemble atoms and provides a robust way\nof creating GHZ states.\n

Quantum controlled-phase-flip (CPF) gate between a flying photon qubit and a stationary atomic qubit could allow the linking of distant computational nodes in a quantum network. Here we present a scheme to realize quantum CPF gate between a flying optical photon and an atomic ensemble based on cavity input-output process and Rydberg blockade. When a flying single-photon pulse is reflected off the cavity containing a Rydberg atomic ensemble, the dark resonance and Rydberg blockade induce a conditional phase shift for the photon pulse, thus we can achieve the CPF gate between the photon and the atomic ensemble. Assisted by Rydberg blockade interaction, our scheme works in the N-atoms strong-coupling regime and significantly relaxes the requirement of strong coupling of single atom to photon in the optical cavity.