We prove that the ground states of a local Hamiltonian satisfy an area law and can be computed in polynomial time when the interaction graph is a tree with discrete fractal dimension $\beta<2$. This condition is met for generic trees in the plane and for established models of hyperbranched polymers in 3D. This work is the first to prove an area law and exhibit a provably polynomial-time classical algorithm for local Hamiltonian ground states beyond the case of spin chains. Our algorithm outputs the ground state encoded as a multi-scale tensor network on the META-tree, which we introduce as an analogue of Vidal's MERA. Our results hold for polynomially degenerate and frustrated ground states, matching the state of the art for local Hamiltonians on a line.

We construct quantum MDS codes for quantum systems of dimension $q$ of length $q^2+1$ and minimum distance $d$ for all $d \leqslant q+1$, $d \neq q$. These codes are shown to exist by proving that there are classical generalised Reed-Solomon codes which are contained in their Hermitian-dual. These constructions include many constructions which were previously known but in some cases these codes appear to be new. We go on to prove that if $d\geqslant q+2$ then there in no generalised Reed-Solomon code which is contained in its Hermitian dual. We also construct a $ [\![ 18,0,10 ]\!]_5$ quantum MDS code, a $ [\![ 18,0,10 ]\!] _7$ quantum MDS code and a $ [\![ 14,0,8 ]\!]_5$ quantum MDS code, which are the first quantum MDS codes discovered for which $d \geqslant q+3$, apart from the $ [\![ 10,0,6 ]\!]_3$ quantum MDS code derived from Glynn's code.

Dynamical quantum phase transition (DQPT) is a periodic phase transition in large quantum systems wherein certain physical quantities show non-analyticity at a particular time $t_c$. We show by exact RG analysis of the quantum Ising model on scale invariant lattices of different dimensions that DQPT may involve fixed points of renormalization group which are unphysical in thermal phase transitions, and, in such cases, boundary conditions may become relevant. The transition points are determined exactly. A counter-example is also given that an equilibrium thermal phase transition does not necessarily imply a DQPT.

Vector vortex beams possess a topological property that derives both from the spatially varying amplitude of the field and also from its varying polarization. This property arises as a consequence of the inherent Skyrmionic nature of such beams and is quantified by the associated Skyrmion number. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the Skyrmion number in this context

Comprehending the dynamical behaviour of quantum systems driven by time-varying Hamiltonians is particularly difficult. Systems with as little as two energy levels are not yet fully understood. Since the inception of Magnus' expansion in 1954, no fundamentally novel mathematical method for solving the quantum equations of motion with a time-varying Hamiltonian has been devised. We report here of an entirely different non-perturbative approach, termed path-sum, which is always guaranteed to converge, yields the exact analytical solution in a finite number of steps for finite systems and is invariant under scale transformations of the quantum state space. Path-sum can be combined with any state-space reduction technique and can exactly reconstruct the dynamics of a many-body quantum system from the separate, isolated, evolutions of any chosen collection of its sub-systems. As examples of application, we solve analytically for the dynamics of all two-level systems as well as of a many-body Hamiltonian with a particular emphasis on NMR (Nuclear Magnetic Resonance) applications: Bloch-Siegert effect and $N$-spin systems involving the dipolar Hamiltonian and spin diffusion.

We aim to devise feasible, efficient verification schemes for bosonic channels. To this end, we construct an average-fidelity witness that yields a tight lower bound for average fidelity plus a general framework for verifying optimal quantum channels. For both multi-mode unitary Gaussian channels and single-mode amplification channels, we present experimentally feasible average-fidelity witnesses and reliable verification schemes, for which sample complexity scales polynomially with respect to all channel specification parameters. Our verification scheme provides an approach to benchmark the performance of bosonic channels on a set of Gaussian-distributed coherent states by employing only two-mode squeezed vacuum states and local homodyne detections. Our results demonstrate how to perform feasible tests of quantum components designed for continuous-variable quantum information processing.

For a quantum pure state in conformal field theory, we generate the Shannon entropy of its coherence, that is, the von Neumann entropy obtained by introducing quantum measurement errors. We give a holographic interpretation of this Shannon entropy, based on Swingle's interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in the context of AdS$_3$/CFT$_2$. As the result, we conjecture a differential geometrical formula of the Shannon entropy as the sum of the Alishahiha complexity and the abbreviated action, divided by $\pi\hbar$, in the bulk domain enclosed by the Ryu-Takayanagi curve.

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the \textit{s}-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially, which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). In this way, such a hybrid system operates as an ultra-sensitive force sensor which can amplify the input signal and simultaneously suppress the added noises by controlling the amplitudes of modulation and the system cooperativities. The advantage of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities is the enhancement of signal amplification as well as the extension of amplification bandwidth.

Author(s): D. B. Horoshko, L. La Volpe, F. Arzani, N. Treps, C. Fabre, and M. I. Kolobov

We study the Bloch-Messiah reduction of parametric down-conversion of light in the pulsed regime with a nondegenerate phase matching providing generation of twin beams. We find that in this case every squeezing eigenvalue has multiplicity at least two. We discuss the problem of ambiguity in the defi...

[Phys. Rev. A 100, 013837] Published Thu Jul 18, 2019

Author(s): Ling-Na Wu and André Eckardt

We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growt...

[Phys. Rev. Lett. 123, 030602] Published Thu Jul 18, 2019

Using a laser, a high-speed detector, and an array of tiny movable mirrors, researchers can reconstruct an image of a hidden object in under a second.

[Physics] Published Thu Jul 18, 2019

Categories: Physics

Author(s): Feihao Zhang, Jiang Zhang, Pan Gao, and Guilu Long

Nonadiabatic holonomic quantum computation (NHQC) offers a way to realize geometric quantum gates beyond the adiabatic regime. To extend the flexibility and control robustness, many NHQC schemes have been proposed. Here, we propose to use quantum optimal control theory to search control sequences th...

[Phys. Rev. A 100, 012329] Published Thu Jul 18, 2019

We demonstrate time-resolved nonlinear extreme-ultraviolet absorption spectroscopy on multiply charged ions, here applied to the doubly charged neon ion, driven by a phase-locked sequence of two intense free-electron laser pulses. Absorption signatures of resonance lines due to 2$p$--3$d$ bound--bound transitions between the spin-orbit multiplets $^3$P$_{0,1,2}$ and $^3$D$_{1,2,3}$ of the transiently produced doubly charged Ne$^{2+}$ ion are revealed, with time-dependent spectral changes over a time-delay range of $(2.4\pm0.3)\,\text{fs}$. Furthermore, we observe 10-meV-scale spectral shifts of these resonances owing to the AC Stark effect. We use a time-dependent quantum model to explain the observations by an enhanced coupling of the ionic quantum states with the partially coherent free-electron-laser radiation when the phase-locked pump and probe pulses precisely overlap in time.

In trapped-ion quantum information processing, interactions between spins (qubits) are mediated by collective modes of motion of an ion crystal. While there are many different experimental strategies to design such interactions, they all face both technical and fundamental limitations to the achievable coherent interaction strength. In general, obtaining strong interactions and fast gates is an ongoing challenge. Here, we extend previous work [Phys. Rev. Lett. 112, 030501 (2019)] and present a general strategy for enhancing the interaction strengths in trapped-ion systems via parametric amplification of the ions' motion. Specifically, we propose a stroboscopic protocol using alternating applications of parametric amplification and spin-motion coupling. In comparison with the previous work, we show that the current protocol can lead to larger enhancements in the coherent interaction that increase exponentially with the gate time.

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible. In this study we propose a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS. This is based on spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems. We show that quantum time crystals are stable to local perturbations at zero temperature. Finally, we reveal the intrinsic connection between continuous and discrete TTS, thus linking the two realms.

Single-photon super- and subradiance are important for the quantum memory and quantum information. We investigate one-dimensional atomic arrays under the spatially periodic magnetic field with a tunable phase, which provides a distinctive physics aspect of revealing exotic two-dimensional topological phenomena with a synthetic dimension. A butterfly-like nontrivial bandstructure associated with the non-Hermitian physics involving strong long-range interactions has been discovered. It leads to pairs of topologically-protected edge states, which exhibit the robust super- or subradiance behavior, localized at the boundaries of the atomic arrays. This work opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions pointing to potential implications for quantum sensing as well as the super-resolution imaging.

We investigate the coherence of quantum channels and establish a resource theory for quantifying the coherence of quantum channels via Choi matrix. To this aim, we define the incoherent channels and incoherent superchannels. This theory recovers the case of quantum states when we view quantum states as a special case of quantum channels and also, this theory allows some analytical expressions for coherence measures.

Recent works have shown that the spectroscopic access to highly-excited states provides enough information to characterize transition states in isomerization reactions. Here, we show that the transition state of the bond breaking HCN-HNC isomerization reaction can also be achieved with the two-dimensional limit of the algebraic vibron model. We describe the system's bending vibration with the algebraic Hamiltonian and use its classical limit to characterize the transition state. Using either the coherent state formalism or a recently proposed approach by Baraban et al. [ Science 2015 , 350 , 1338], we obtain an accurate description of the isomerization transition state. In addition, we show that the energy level dynamics and the transition state wave function structure indicate that the spectrum in the vicinity of the isomerization saddle point can be understood in terms of the formalism for excited state quantum phase transitions.

Understanding and controlling exciton transport is a strategic way to enhance the optoelectronic properties of high-performance organic devices. In this article we study triplet exciton migration in crystalline poly($p$-phenylene vinylene) polymer (PPV) using comprehensive electronic structure and quantum dynamical methods. We solve the coupled electron-nuclear dynamics for the triplet energy migrating between two neighboring Frenkel sites in J- and H-aggregate arrangements. From the two-site model we extract key parameters for use with a master-equation approach that allows us to treat nanosize systems where time-dependent Schr\"odinger equation becomes intractable. We calculate the transient exciton density evolution and determine the diffusion constants along the principal crystal axes of the PPV. The triplet diffusion is characterized by two distinctive components: fast intrachain, and slow interchain. At room temperature the interchain diffusion coefficients are found to be $D_a=0.89\cdot10^{-2}$ cm$^2$s$^{-1}$ and $D_b=1.49\cdot10^{-2}$ cm$^2$s$^{-1}$ along the respective $\bar{a}$- and $\bar{b}$-axes, and the intrachain is $D_c=3.03$ cm$^2$s$^{-1}$ along the fast $\bar{c}$-axis. The exceptionally high exciton mobility along the $\pi$-conjugated backbone facilitates rapid triplet migration over long distances. Our results can be utilized in the design of efficient energy conversion and light-emitting devices with desired solid-state properties.

Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian quantum theory is envisioned to have far-reaching implications and applications. It is known that the PT-inner product is defined with respect to a non-canonical, system generated symmetry, namely the C symmetry. We show that the PT symmetric equation of motion is defined by the simultaneous time evolution of the state $\psi(t)$ and the operator C(t) to manifests unitarity - a situation analogous to the Dirac/interaction picture. The time-dependent C operator lends itself into a new term in the Berry phase, setting a platform for novel and exotic topological phases. We also point out that the gauge invariance is achieved by a more generic CPT gauge transformation, not by the usual unitary gauge transformation. The PT symmetric theory is not generally applicable for spin-1/2 fermions, since here PT inner product becomes undefined due to Kramer's theory. We propose a realizable non-Hermitian setup for spin-1/2 fermions which acquires the combined PT^2=+1 symmetry, despite T^2=-1 and P^2=+1. The Hamiltonian inherits non-Abelian Berry gauge fields for non-interacting fermions without magnetic field. The corresponding edge states are found to have unique supersymmetric oscillator solutions but with complex energy levels.