We present numerical studies of quantum walks on ${\text{C}}_{60}$ and related graphene structures to investigate their transport properties. Also known as a honeycomb lattice, the lattice formed by carbon atoms in the graphene phase can be rolled up to form nanotubes of various dimensions. Graphene nanotubes have many important applications, some of which rely on their unusual electrical conductivity and related properties. Quantum walks on graphs provide an abstract setting in which to study such transport properties independent of the other chemical and physical properties of a physical substance. They can thus be used to further the understanding of mechanisms behind such properties. We find that nanotube structures are significantly more efficient in transporting a quantum walk than cycles of equivalent size, provided the symmetry of the structure is respected in how they are used. We find faster transport on zigzag nanotubes compared to armchair nanotubes, which is unexpected given that for the actual materials the armchair nanotube is metallic, while the zigzag is semiconducting.

In this work we introduce an original scheme for measurement based quantum computation in continuous variables. Our approach does not necessarily rely on the use of ancillary cluster states to achieve its aim, but rather on the detection of a resource state in a suitable mode basis followed by digital postprocessing, and involves an optimization of the adjustable experimental parameters. After introducing the general method, we present some examples of application to simple specific computations.

Here I present a method for how intersections of a certain density matrix of rank 2 with the zero polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely, in terms of the Bloch-sphere analogy, solves this problem immediately. To this end, I determine the zero polytope of the three-tangle, which is an exact result up to computer accuracy, and calculate upper bounds to its convex roof which are below the linearized upper bound. The zeros of the three-tangle (in this case) induced by the zero polytope (zero simplex) are exact values. I apply this procedure to a superposition of the four-qubit Greenberger-Horne-Zeilinger and $W$ state. It can, however, be applied to every case one has under consideration, including an arbitrary polynomial convex-roof measure of entanglement and for arbitrary local dimension.

In this paper we derive basic properties of the Green's-function matrix elements stemming from the exponential coupled-cluster (CC) parametrization of the ground-state wave function. We demonstrate that all intermediates used to express the retarded (or, equivalently, ionized) part of the Green's function in the $\omega$ representation can be expressed only through connected diagrams. Similar properties are also shared by the first-order $\omega$ derivative of the retarded part of the CC Green's function. Moreover, the first-order $\omega$ derivative of the CC Green's function can be evaluated analytically. This result can be generalized to any order of $\omega$ derivatives. Through the Dyson equation, derivatives of the corresponding CC self-energy operator can be evaluated analytically. In analogy to the CC Green's function, the corresponding CC self-energy operator can be represented by connected terms. Our analysis can easily be generalized to the advanced part of the CC Green's function.

A relativistic description of the structure of heavy alkali-metal atoms and alkali-like ions using S-spinors and L-spinors is developed. The core wave function is defined by a Dirac-Fock calculation using an S-spinor basis. The S-spinor basis is then supplemented with a large set of L-spinors for calculation of the valence wave function in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s, 4d$, and $5p$ states of ${\mathrm{Sr}}^{+}$. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the $5s\to 4d_{\frac{3}{2}}$ and $5s\to 4d_{\frac{5}{2}}$ transitions near 417 nm (near the wavelength for the $5s\to 5p_j$ transitions) would allow determination of the oscillator strength ratio for the $5s\to 5p_{\frac{1}{2}}$ and $5s\to 5p_{\frac{3}{2}}$ transitions.

Cooling vibrational degrees of freedom down to ground states is essential to observation of quantum properties of systems with mechanical vibration. We propose two cooling schemes employing four internal levels of the systems, which achieve the ground-state cooling in an efficient fashion by completely deleting the carrier and first-order blue-sideband transitions. The schemes, based on quantum interference and Stark-shift gates, are robust to fluctuations of laser intensity and frequency. The feasibility of the schemes is justified using current laboratory technology. In practice, our proposal readily applies to a nanodiamond nitrogen-vacancy center levitated in an optical trap or attached to a cantilever.

We study theoretically the effect of giant resonance in Xe on the phase difference between consecutive resonantly enhanced high-order harmonics and calculate the duration of the attosecond pulses produced by these harmonics. For certain conditions, resonantly induced dephasing compensates the phase difference which is intrinsic for off-resonance harmonics. We find these conditions analytically and compare them with numerical results. This harmonic synchronization allows attosecond-pulse shortening in conjunction with the resonance-induced intensity increase of more than an order of magnitude. The latter enhancement relaxes the requirements for the UV filtering needed for attosecond-pulse production. Using a two-color driving field allows a further increase of the intensity. In particular, a causticlike feature in the harmonic spectrum leads to a generation efficiency growth of up to two orders of magnitude, which is, however, accompanied by an elongation of the XUV pulse.

This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to know the correct form of the equations which play similar roles to the Navier-Stokes equation in classical turbulence. Here, such equations are obtained by carefully taking into account the frequently overlooked multivalued nature of the $U\left(1\right)$ phase field. Such an approach provides exact analytical explanations to some numerically observed features involving the dynamics of quantum vortices in Bose-Einstein condensates, such as the universal $t^{1/2}$ behavior of reconnecting vortex lines. It also expands these results beyond the Gross-Pitaevskii theory so that some features can be generalized to other systems such as superfluid ${}^4\mathrm{He}$, dipolar condensates, and mixtures of different superfluid systems.

We study experimentally the stability of excited, interacting states of bosons in a double-well optical lattice in regimes where the nonlinear interactions are expected to induce “swallowtail” looped band structure. A dynamic homogeneous Gross-Pitaevskii calculation indicates that the double-well lattice both stabilizes the looped band structure and allows for dynamic preparation of different initial states, including states within the loop structure. The homogeneous calculation predicts that the loop states, unlike the ground states, should be dynamically stable. An inhomogeneous mean-field calculation including the trap potential, however, implies that the decay is dominated by inhomogeneous effects and that there is little variation in the decay rate among the states prepared within the loop structure. By experimentally preparing different initial coherent states and observing their subsequent decay, we observe distinct decay rates in regimes where multivalued looped band structure is expected, although not the stability predicted by the homogeneous calculation.

We study the expansion of an interacting atomic system at zero temperature, following its release from an isotropic three-dimensional harmonic trap and calculate the time dependence of its density and momentum distribution, with special focus on the behavior of the contact parameter. We consider different quantum systems, including the unitary Fermi gas of infinite scattering length, the weakly interacting Bose gas, and two interacting particles with highly asymmetric mass imbalance. In all cases analytic results can be obtained, which show that the initial value of the contact, fixing the $1/k^4$ tail of the momentum distribution, disappears for large expansion times. Our results raise the problem of understanding the recent experiment of R. Chang et al. [Phys. Rev. Lett. 117, 235303 (2016)] carried out on a weakly interacting Bose gas of metastable ${}^4\mathrm{He}$ atoms, where a $1/r^4$ tail in the density distribution was observed after a large expansion time, implying the existence of the $1/k^4$ tail in the asymptotic momentum distribution.

Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with postselected measurement results. In these cases, only a part of the Hilbert space needs to be represented, and one can define this restriction by way of a projection operator. Here coherent state bases and normally ordered phase-space representations are introduced for treating such projected Hilbert spaces, including existence theorems and dynamical equations. These techniques are very useful in studying novel optical or microwave integrated photonic quantum technologies, such as boson sampling or Josephson quantum computers. In these cases, states become strongly restricted due to inputs, nonlinearities, or conditional measurements. This paper focuses on coherent phase states, which have especially simple properties. Practical applications are reported on calculating recurrences in anharmonic oscillators, the effects of arbitrary phase noise on Schrödinger cat fringe visibility, and on boson sampling interferometry for large numbers of modes.

Hybrid quantum systems can often be described in terms of polaritons. These are quasiparticles formed of superpositions of their constituents, with relative weights depending on some control parameter in their interaction. In many cases, these constituents are coupled to reservoirs at different temperatures. This suggests a general approach to the realization of polaritonic heat engines where a thermodynamic cycle is realized by tuning this control parameter. Here we discuss what is arguably the simplest such engine, a single qubit coupled to a single photon. We show that this system can extract work from feeble thermal microwave fields. We also propose a quantum measurement scheme of the work and evaluate its backaction on the operation of the engine.

We study phonon statistics in a nanomechanical resonator (NAMR) which is resonantly coupled to a qubit. We find that there are two different mechanisms for phonon blockade in such a resonantly coupled NAMR-qubit system. One is due to the strong anharmonicity of the NAMR-qubit system with large coupling strength; the other one is due to the destructive interference between different paths for two-phonon excitation in the NAMR-qubit system with a moderate coupling strength. We find that the phonon blockade is fragile towards thermal mode occupations and can only be observed for NAMR being at ultracold effective temperature. In order to enlarge the mean phonon number for strong phonon antibunching with a moderate NAMR-qubit coupling strength, we assume that two external driving fields are applied to the NAMR and qubit, respectively. In this case, we find that the phonon blockades under two mechanisms can appear at the same frequency regime by optimizing the strength ratio and phase difference of the two external driving fields.

For multilevel spin systems, robustness of the quantum mechanical (QM) violation of macrorealism (MR) with respect to coarse-grained measurements is investigated using three different necessary conditions of MR, namely, the Leggett-Garg inequality (LGI), Wigner's form of the Leggett-Garg inequality (WLGI), and the condition of no-signaling in time (NSIT). It is shown that for dichotomic sharp measurements, in the asymptotic limit of spin, the algebraic maxima of the QM violations of all these three necessary conditions of MR are attained. Importantly, the QM violations of all these persist in that limit even for arbitrary unsharp measurements, i.e., for any nonzero value of the sharpness parameter characterizing the degree of fuzziness of the relevant measurements. We also find that, when different measurement outcomes are clubbed into two groups for the sake of dichotomizing the outcomes, the asymmetry or symmetry in the number of outcomes in the two groups, signifying the degree of coarse graining of measurements, has a crucial role in discerning quantum violation of MR. The results clearly demonstrate that classicality does not emerge in the asymptotic limit of spin, whatever be the unsharpness and degree of coarse graining of the measurements.

There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-time-ordered (OTO) correlation functions such as $\langle O_2\left(t\right)O_1\left(0\right)O_2\left(t\right)O_1\left(0\right)\rangle$ is a faithful measure of quantum chaos. Experimentally, these correlators are challenging to access since they apparently require access to both forward and backward time evolution with the system Hamiltonian. Here we propose a protocol to measure such OTO correlators using an ancilla that controls the direction of time. Specifically, by coupling the state of the ancilla to the system Hamiltonian of interest, we can emulate the forward and backward time propagation, where the ancilla plays the role of a quantum clock. Within this scheme, the continuous evolution of the entire system (the system of interest and the ancilla) is governed by a time-independent Hamiltonian. We discuss the implementation of our protocol with current circuit-QED technology for a class of interacting Hamiltonians. Our protocol is immune to errors that could occur when the direction of time evolution is externally controlled by a classical switch.

Reference-frame-independent quantum key distribution (RFI QKD) has been experimental demonstrated to be robust for slowly varying reference frames. However, the protocol fails when reference frame varies rapidly. Furthermore, the rigorous definition of “slowly varying” is still not clear. Here we analyze the relationship of the related parameters and show how to adjust these parameters to make RFI QKD to be valid. This work provides a clear valid condition for the RFI QKD protocol and opens a way for researchers and users to handle the RFI QKD process practically.

We report on a resonantly coupled 2(1)-4(1) photoassociation resonance in LiRb. This pair of states displays interesting decay physics that hint at interference-like effects caused by two different decay paths. We observe decay to predominantly $X{}^1{\mathrm{\Sigma }}^{+}v=43$, with significant numbers of molecules produced in $X{}^1{\mathrm{\Sigma }}^{+}v=2-12$. This photoassociation resonance also produces $\sim 300 X{}^1{\mathrm{\Sigma }}^{+}v=0J=0$ molecules/s. Finally, we identify a stimulated Raman adiabatic passage transfer pathway from $v=43$ to $v=0$ that has the potential to produce up to $2\times {10}^5$ LiRb molecules/s in the $X{}^1{\mathrm{\Sigma }}^{+}v=0J=0$ state.

It was recently shown [G. Albareda et al., Phys. Rev. Lett. 113, 083003 (2014)] that within the conditional decomposition approach to the coupled electron-nuclear dynamics, the electron-nuclear wave function can be exactly decomposed into an ensemble of nuclear wave packets effectively governed by nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system, we show that for strong nonadiabatic couplings the nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer potential-energy surfaces. The nature of these steps is identified as an effect of electron-nuclear correlation. Furthermore, a direct comparison with similar discontinuities recently reported in the context of the exact factorization framework allows us to draw conclusions about the universality of these discontinuities, viz., they are inherent to all nonadiabatic nuclear dynamics approaches based on (exact) time-dependent potential-energy surfaces.

We consider two interacting bosons in a dimerized Su-Schrieffer-Heeger (SSH) lattice. We identify a rich variety of two-body states. In particular, for open boundary conditions and moderate interactions, edge bound states (EBS) are present even for the dimerization that does not sustain single-particle edge states. Moreover, for large values of the interactions, we find a breaking of the standard bulk-boundary correspondence. Based on the mapping of two interacting particles in one dimension onto a single particle in two dimensions, we propose an experimentally realistic coupled optical fibers setup as quantum simulator of the two-body SSH model. This setup is able to highlight the localization properties of the states as well as the presence of a resonant scattering mechanism provided by a bound state that crosses the scattering continuum, revealing the closed-channel population in real time and real space.

Using multilevel (161-level) numerical simulations beyond the rotating-wave approximation, we investigate the single-atom response of helium to intense pulses of radiation with properties characteristic of a self-amplified spontaneous emission (SASE) free-electron laser (FEL) source, and central wavelengths resonant with $1snp$ excitation ($n=3$,4). The results show a complete breakdown of the two-level approximation and suggest that, under typical experimental conditions, levels other than the resonant level are significantly populated. We discuss the implications for the subsequent development of superfluorescence (a collective effect) from the excited atomic medium and compare the results to recent experiments.