We present first results from a number of experiments conducted on a 0.53-kg cylindrical dumbbell-shaped sapphire crystal. Here we report on an optomechanical experiment utilizing a modification to the typical cylindrical architecture. Mechanical motion of the crystal structure alters the dimensions of the crystal, and the induced strain changes the permittivity. These two effects result in parametric frequency modulation of resonant microwave whispering gallery modes that are simultaneously excited within the crystal. A microwave readout system is implemented, allowing extremely low noise measurements of this frequency modulation near our modes of interest, having a phase noise floor of $-165$ dBc/Hz at 100 kHz. Fine tuning of the crystal's suspension has allowed for the optimization of mechanical quality factors in preparation for cryogenic experiments, with a value of $Q=8\times {10}^7$ achieved at 127 kHz. This results in a $Q\times f$ product of ${10}^{13}$, equivalent to the best measured values in a macroscopic sapphire mechanical system. Results are presented that demonstrate the excitation of mechanical modes via radiation pressure force, allowing an experimental method of determining the transducer's displacement sensitivity $df/dx$ and calibrating the system. Finally, we demonstrate parametric backaction phenomenon within the system. These are all important steps towards the goal of achieving quantum limited measurements of a kilogram-scale macroscopic device for the purpose of detecting deviations from standard quantum theory resulting from quantum gravitational effects.

Systems of interacting classical harmonic oscillators have received considerable attention in the past years as analog models for describing electromagnetically induced transparency (EIT) and associated phenomena. We review these models and investigate their validity for a variety of physical systems using two and three coupled harmonic oscillators. From the simplest EIT-$\mathrm{\Lambda }$ configuration and two coupled single cavity modes we show that each atomic dipole-allowed transition and a single cavity mode can be represented by a damped harmonic oscillator. Thus, we have established a one-to-one correspondence between the classical and quantum dynamical variables. We show the limiting conditions and the equivalent for the EIT dark state in the mechanical system. This correspondence is extended to other systems that present EIT-related phenomena. Examples of such systems are two- and three-level (cavity EIT) atoms interacting with a single mode of an optical cavity and four-level atoms in a inverted-Y and tripod configurations. The established equivalence between the mechanical and the cavity EIT systems has been corroborated by experimental data. The analysis of the probe response of all these systems also brings to light a physical interpretation for the expectation value of the photon annihilation operator $〈a〉$. We show that it can be directly related to the electric susceptibility of systems, the composition of which includes a driven cavity-field mode.

The Bell test is one of the most important tools in quantum information science. On the one hand, it enables fundamental tests of the basic physics laws of nature, and on the other hand, it can also be applied in a variety of device-independent tasks such as quantum key distribution and random number generation. In practice, loopholes existing in experimental demonstrations of Bell tests may affect the validity of the conclusions. In this work, we focus on the randomness (freewill) loophole and investigate the randomness requirement in a well-known Bell test, the Clauser-Horne test, under various conditions. We explicitly bound the Bell value for all local hidden variable models by optimizing over all classical strategies exploiting the knowledge of the partially random inputs. Our result thus provides input randomness requirements on the Clauser-Horne test under varieties of practical scenarios. The employed analysis technique can also be generalized to other Bell inequalities.

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. In particular, we generally prove that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables. These results add to the list of well-known properties of coherent states and are applied here to the Lipkin-Meshkov-Glick model, the Dicke model, and to coherent intertwiners in spin networks as considered in loop quantum gravity.

We consider the use of quantum error-detecting codes, together with energy penalties against leaving the code space, as a method for suppressing environmentally induced errors in Hamiltonian-based quantum computation. This method was introduced in Jordan et al. [Phys. Rev. A 74, 052322 (2006)] in the context of quantum adiabatic computation, but we consider it more generally. Specifically, we consider a computational Hamiltonian, which has been encoded using the logical qubits of a single-qubit error-detecting code, coupled to an environment of qubits by interaction terms that act one-locally on the system. Additional energy penalty terms penalize states outside of the code space. We prove that in the limit of infinitely large penalties, one-local errors are completely suppressed, and we derive some bounds for the finite penalty case. Our proof technique involves exact integration of the Schrodinger equation, making no use of master equations or their assumptions. We perform long time numerical simulations on a small (one logical qubit) computational system coupled to an environment and the results suggest that the energy penalty method achieves even greater protection than our bounds indicate.

We propose and analyze a high-fidelity readout scheme for a single-instance approach to quantum computing in rare-earth-ion-doped crystals. The scheme is based on using different elements as qubit and readout ions, where the readout ions are doped into the material at a much lower concentration than the qubit ions. It is shown that by allowing the qubit ion sitting closest to a readout ion to act as a readout buffer, the readout error can be reduced by more than an order of magnitude. The scheme is shown to be robust against certain experimental variations, such as varying detection efficiencies, and we use the scheme to predict the attainable quantum fidelity of a controlled not (cnot) gate in these solid-state systems. In addition, we discuss the potential scalability of the protocol to larger qubit systems. The results are based on parameters which we believe are experimentally feasible with current technology and which can be simultaneously realized.

To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfill for superconducting qubits and appears to be a main reason why only single-qubit gates were implemented in a recent experiment [A. A. Abdumalikov, Jr. et al., Nature (London) 496, 482 (2013)]. Here we propose to realize nonadiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a minimal resource for the decoherence-free subspace encoding. In particular, our scheme not only overcomes the difficulties encountered in previous studies but also can still achieve considerably large effective coupling strength, such that high-fidelity quantum gates can be achieved. Therefore, the present scheme makes realizing robust holonomic quantum computation with superconducting circuits very promising.

There exists two prominent methods to transfer information between two spatially separated parties, namely Alice (A) and Bob (B): quantum teleportation and remote state preparation. However, the difference between these methods is, in the teleportation scheme, the state to be transferred is completely unknown, whereas in state preparation it should be known to the sender. In addition, photonic state teleportation is probabilistic due to the impossibility of performing a two-particle complete Bell-state analysis with linear optics, while remote state preparation can be performed deterministically. Here we report the first realization of photonic hybrid remote state preparation from spin to orbital angular momentum degrees of freedom. In our scheme, the polarization state of photon A is transferred to orbital angular momentum of photon B. The prepared states are visualized in real time by means of an intensified CCD camera. The quality of the prepared states is verified by performing quantum state tomography, which confirms an average fidelity higher than 99.4%. We believe that this experiment paves the way towards a novel means of quantum communication in which encryption and decryption are carried out in naturally different Hilbert spaces, and therefore may provide a means for enhancing security.

We investigate how much amount of Greenberger-Horne-Zeilinger (GHZ) entanglement is required in order to prepare a given multipartite state by local operations and classical communication (LOCC). We present a LOCC procedure that asymptotically converts GHZ states into an arbitrary multipartite pure state, whose conversion rate is given by the multipartite discord of the state. This reveals that the GHZ-entanglement cost of preparing a pure state is not higher than the multipartite discord of the state. It also provides an operational interpretation of multipartite discord for pure states, namely, the consumption rate of GHZ entanglement in the devised procedure.

We investigate quantum metrology using a Lie algebraic approach for a class of Hamiltonians, including local and nearest-neighbor interaction Hamiltonians. Using this Lie algebraic formulation, we identify and construct highly symmetric states that admit Heisenberg scaling in precision for phase estimation in the absence of noise. For the nearest-neighbor Hamiltonian we also perform a numerical scaling analysis of the performance of pretty good states and derive upper bounds on the quantum Fisher information.

Here, we study the classical information capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. We present a formula for general channel capacity and show that this capacity is achieved without requiring the use of entangling operations typically required for scalable universal quantum computation, e.g., Knill-Laflamme-Milburn measurement-assisted transformations. As an example, we provide an explicit encoding scheme using the resources required of standard dense coding using two dual-rail qubits (two photons in four modes). In this case, our protocol encodes one additional bit of information. Greater gains are expected for larger systems.

Dynamical decoupling is a powerful method for protecting quantum information against unwanted interactions with the help of open-loop control pulses. Realistic control pulses are not ideal and may introduce additional systematic errors. We introduce a class of self-stabilizing pulse sequences capable of suppressing such systematic control errors efficiently in qubit systems. Embedding already known decoupling sequences into these self-stabilizing sequences offers powerful means to achieve robustness against unwanted external perturbations and systematic control errors. As these self-stabilizing sequences are based on single-qubit operations, they offer interesting perspectives for future applications in quantum information processing.

Radiative corrections to an atom are calculated near a half-space that has arbitrarily shaped small depositions upon its surface. The method is based on calculation of the classical Green's function of the macroscopic Maxwell equations near an arbitrarily perturbed half-space using a Born-series expansion about the bare half-space Green's function. The formalism of macroscopic quantum electrodynamics is used to carry this over into the quantum picture. The broad utility of the calculated Green's function is demonstrated by using it to calculate two quantities: the spontaneous decay rate of an atom near a sharp surface feature and the Casimir-Polder potential of a finite grating deposited on a substrate. Qualitatively different behavior is found for the latter case where it is observed that the periodicity of the Casimir-Polder potential persists even outside the immediate vicinity of the grating.

We have developed a two-electron outer region for use within $R$-matrix theory to describe double ionization processes. The capability of this method is demonstrated for single-photon double ionization of He in the photon energy region between 80 and 180 eV. The cross sections are in agreement with established data. The extended $R$-matrix with time dependence method also provides information on higher-order processes, as demonstrated by the identification of signatures for sequential double ionization processes involving an intermediate ${\mathrm{He}}^{+}$ state with $n=2$.

We report the measurement of the deca-heptuplet $s$-partial-wave scattering length $a$ of two bosonic isotopes of the highly magnetic element dysprosium: $a=112\left(10\right)a_0$ for ${}^{162}\mathrm{Dy}$ and $a=92\left(8\right)a_0$ for ${}^{164}\mathrm{Dy}$, where $a_0$ is the Bohr radius. The scattering lengths are determined by the cross-dimensional relaxation of ultracold gases of these Dy isotopes at temperatures above quantum degeneracy. In this temperature regime, the measured rethermalization dynamics can be compared to simulations of the Boltzmann equation using a direct-simulation Monte Carlo method employing the anisotropic differential scattering cross section of dipolar particles.

Calculations of the photoionization cross section of the $2p$ and $3s$ subshells of free Ar and Ar@${\mathrm{C}}_{60}$ as examples have been performed using the molecular structure of the confined system and time-dependent density functional theory for the dynamical quantities. The results for $\mathrm{Ar}2p$ in the combined system exhibit significant confinement resonances with the lower-energy ones being quite sharp, in contrast to the results of jellium-model calculations. In addition, calculations done with and without interchannel coupling between the photoionization channels of the $2p$ subshell of the Ar atom and the $1s$ subshell of the ${\mathrm{C}}_{60}$ shell show that, in this case, the coupling is of negligible importance, even though the $\mathrm{C}1s$ cross section is more than an order of magnitude larger than that of $\mathrm{Ar}2p$ in the 300 eV range. The $\mathrm{Ar}3s$, which is not hybridized, also exhibits confinement resonances, but is very strongly affected by interchannel coupling with photoionization channels from the ${\mathrm{C}}_{60}$ shell. The phenomenology of both $2p$ and $3s$ subshells is explained in terms of the interchannel-coupling matrix elements. These results should be applicable to inner-shell ionization of essentially any endohedral fullerene system.

We investigate high-order-harmonic spectra from aligned diatomic molecules in intense driving fields whose components have orthogonal polarizations. We focus on how the driving-field ellipticity influences structural interference patterns in a macroscopic medium. In a previous publication [Phys. Rev. A 88, 023404 (2013)] we have shown that the nonvanishing ellipticity introduces an effective dynamic shift in the angle for which the two-center interference maxima and minima occur, with regard to the existing condition for linearly polarized fields. In this work we show through simulation that it is still possible to observe this shift in harmonic spectra that have undergone macroscopic propagation, and discuss the parameter range for doing so. These features are investigated for ${\mathrm{H}}_2$ in a bichromatic field composed of two orthogonally polarized waves. The shift is visible both in the near- and in the far-field regime, so that, in principle, it can be observed in experiments.

The nature of light-induced structures in attosecond transient-absorption spectroscopy of molecular systems is investigated theoretically. It is shown how nuclear dynamics affect these structures. We find that a theoretical three-surface model captures the main characteristics in the calculated spectra. Based on this model, nuclear dynamics is divided into different categories, each category having unique signatures in the absorption spectra. Finally, we discuss the possibility for experimental observation of light-induced structures in molecules.

The tunneling ionization of exotic atoms such as muonic hydrogen, muonium, and positronium in a strong laser field of circular polarization is investigated, taking into account the impact of the motion of the center of mass on the the tunneling ionization dynamics. The momentum partition between the ionization products is deduced. The effect of the center-of-mass motion for the momentum distribution of the ionization components is determined. The effect scales with the ratio of the electron (muon) to the atomic core masses and is nonnegligible for exotic atoms, while being insignificant for common atoms. It is shown that the electron (muon) momentum shift during the under-the-barrier motion due to the magnetically induced Lorentz force has a significant impact on the momentum distribution of the atomic core and depends on the ratio of the electron to the atomic core masses.

We derive an analytic expression for the wavelength scaling of the high-order-harmonic generation (HHG) yield induced by midinfrared driving laser fields. It is based on a quasiclassical description of the returning electron wave packet, which is shown to be largely independent of atomic properties. The accuracy of this analytic expression is confirmed by comparison with results of numerical solutions of the time-dependent Schrödinger equation for wavelengths in the range of $1.4\mu \mathrm{m}⩽\lambda ⩽4\mu \mathrm{m}$. We verify the wavelength scaling of the HHG yield found numerically for midinfrared laser fields in a recent paper by Le et al. [Phys. Rev. Lett. 113, 033001 (2014)].