We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant approach for solving non-Markovian open quantum dynamics in general linear systems.

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.

The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities we find good agreement with the universal results depending only on the scattering length $a_s$, at moderate and high densities the transition temperature is strongly affected by interactions and the excitation spectrum of quasiparticles. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.

We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan’s relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tan’s contact to the momentum $\mathcal{C}/q$. Bragg spectroscopy of ultracold ${}^6\mathrm{Li}$ atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the $f$-sum rule, which is found to improve the accuracy of the structure factor measurement.

We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-$1/2$ nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground-state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models, real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean-field theory.

We conjecture that nonequilibrium boundary conditions generically trigger long-range order in nonequilibrium steady states of locally interacting quantum chains. Our result is based on large scale density matrix renormalization group simulations of several models of quantum spin-$\frac{1}{2}$ chains which are driven far from equilibrium by coupling to a pair of unequal Lindblad reservoirs attached locally to the ends of the chain. In particular, we find a phase transition from exponentially decaying to long-range spin-spin correlations in an integrable Heisenberg $XXZ$ chain by changing the anisotropy parameter. Long-range order also typically emerges after breaking the integrability of the model.

We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the $\pi$ phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed.

A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit of which the gap can be tuned fast and have coupled this qubit strongly to an $LC$ oscillator. We show full spectroscopy of the qubit-oscillator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency ${\nu }_{\mathrm{osc}}$ we find the largest vacuum Rabi splitting of $\sim 0.1{\nu }_{\mathrm{osc}}$. Here being at resonance coincides with the optimal coherence of the symmetry point.

We propose a novel definition of efficiency, valid for motors in a nonequilibrium stationary state exchanging heat and possibly other resources with an arbitrary number of reservoirs. This definition, based on a rational estimation of all irreversible effects associated with power production, is adapted to the concerns of sustainable development. Under conditions of maximum power production the new efficiency has for upper bound $\frac{1}{2}$ in situations relevant for mesoscopic systems. These results imply that at maximum power bithermal, stationary motors could reach a higher Carnot efficiency than the usual cyclic motors.

The current through nanostructures like quantum dots can be stabilized by a classical feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles $n$. At large times, the feedback loop freezes the fluctuations of $n$, which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.

We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense “fault-tolerant” and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.

We propose a method of achieving large temperature $T$ sensitivity in the Casimir force that involves measuring the stable separation between dielectric objects immersed in a fluid. We study the Casimir force between slabs and spheres using realistic material models, and find large $>2\mathrm{nm}/\mathrm{K}$ variations in their stable separations (hundreds of nanometers) near room temperature. In addition, we analyze the effects of Brownian motion on suspended objects, and show that the average separation is also sensitive to changes in $T$. Finally, this approach also leads to rich qualitative phenomena, such as irreversible transitions, from suspension to stiction, as $T$ is varied.

We demonstrate experimentally an efficient coherent rephasing scheme for the storage and recall of weak coherent light pulses in an inhomogeneously broadened optical transition in a ${\mathrm{Pr}}^{3+}:\mathrm{YSO}$ crystal at 2.1 K. Precise optical pumping using a frequency stable ($\approx 1\mathrm{kHz}$ linewidth) laser is employed to create a highly controllable atomic frequency comb structure. We report single photon level storage and retrieval efficiencies of 25%, based on coherent photon-echo-type reemission in the forward direction. The high efficiency is mainly a product of our highly controllable and precise ensemble-shaping technique. The coherence property of the quantum memory is proved through interference between a super-Gaussian pulse and the emitted echo.

Multicomponent quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum dynamics of biomolecular aggregates. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively and standard approaches are invalid or inefficient. Here we combine the time-dependent density matrix renormalization group with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multicomponent systems.

We demonstrate submicron spatial control of interatomic interactions in a Bose-Einstein condensate of ytterbium (Yb). A pulsed optical standing wave, tuned near an optical Feshbach resonance, varies the $s$-wave scattering length continuously across the standing wave pattern. The modulated mean-field energy with a spatial period every 278 nm is monitored by a diffraction pattern in a time-of-flight image. We observe a wide scattering length control of up to 250 nm. The demonstrated spatial modulation of the scattering length proves that high resolution control of atomic interactions is possible.

Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size $L$ in $d$ spatial dimensions is $S\sim L^{d-1}\log L$, a result that should be contrasted with the usual boundary law $S\sim L^{d-1}$. This term depends only on the geometry of the Fermi surface and on the boundary of the region in question. I give an intuitive account of this anomalous scaling based on a low energy description of the Fermi surface as a collection of one-dimensional gapless modes. Using this picture, I predict a violation of the boundary law in a number of other strongly correlated systems.

We propose a theory of adiabaticity in quantum Markovian dynamics based on a decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As two applications of our theory, we propose a general framework for decoherence-assisted computation in noiseless codes and a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by nondissipative means.

We address the problem of quantifying the non-Markovian character of quantum time evolutions of general systems in contact with an environment. We introduce two different measures of non-Markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts. When complete tomographic knowledge about the evolution is available, our measure provides a necessary and sufficient condition to quantify strictly the non-Markovianity. In the opposite case, when no information whatsoever is available, we propose a sufficient condition for non-Markovianity. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.

We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-$3/2$ fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an $\mathrm{SU}(2)\otimes \mathrm{SU}(2)$ symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-$1/2$ Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-$1/2$ gases.

We present a method to synthesize an arbitrary quantum state of two superconducting resonators. This state-synthesis algorithm utilizes a coherent interaction of each resonator with a tunable artificial atom to create entangled quantum superpositions of photon number (Fock) states in the resonators. We theoretically analyze this approach, showing that it can efficiently synthesize NOON states, with large photon numbers, using existing technology.