Stefan Filipp, Erik Sjöqvist
Uhlmann's concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case providing insight into the geometry of state space when the Uhlmann holonomy is undefined. Comparison with previous off-diagonal geometric phase definitions is carried out and an example comprising the transport of a Bell-state mixture is given.
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If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.
Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behavior of the off-diagonal elements of density matrices with respect to the uncertainty principle and to analyze the effects of electron correlation on off-diagonal order. We show that electron correlation induces off-diagonal order in position space which is characterized by larger entropic values. Electron correlation in momentum space is characterized by smaller entropic values as information is forced into regions closer to the diagonal. Related off-dia…
Dynamics of resonant energy transfer of a single excitation in a molecular dimer system is studied in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. It is found that the off-diagonal coupling plays an important role in the excitation energy transfer process. Coherent transfer can be found at arbitrary temperature for a non-vanishing off-diagonal coupling strength with an oscillation frequency of site populations that increases with the off-diagonal coupling strength. Furthermore, we identify a threshold of the off-diagonal coupling strength below which there ex…
In this paper, the off-diagonal geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Increasing temperature tends to suppress the off-diagonal geometric phase, including 1-order and 2-order cases. On the other hand, the relationship between the geometric phase and external magnetic field is discussed.
The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical setting for realizing non-Abelian off-diagonal GPs. The proposed non-Abelian off-diagonal GPs can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions. Our proposal seems to be within reach in various nano-engineered systems and therefore opens up for first experimental test of the non-Abelian off-diagonal GP.
The effect due to the inter-subsystem coupling on the off-diagonal geometric phase in a composite system is investigated. We analyze the case where the system undergo an adiabatic evolution. Two coupled qubits driven by time-dependent external magnetic fields are presented as an example, the off-diagonal geometric phase as well as the adiabatic condition are examined and discussed.
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.
Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed state concept proposed in [Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The first and second order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states.
In this short note we discuss the relation between the so-called Off-Diagonal-Long-Range-Order in many-body interacting quantum systems introduced by C. N. Yang in Rev. Mod. Phys. {\bf 34}, 694 (1962) and entanglement. We argue that there is a direct relation between these two concepts.
Off-diagonal mixed state phases based upon a concept of orthogonality adapted to unitary evolution and a proper normalisation condition are introduced. Some particular instances are analysed and parallel transport leading to the off-diagonal mixed state geometric phase is delineated. A complete experimental realisation of the off-diagonal mixed state geometric phases in the qubit case using polarisation-entangled two-photon interferometry is proposed.
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide a…
The effect of entanglement on off-diagonal geometric phases is investigated in the paper. Two spin-1/2 particles in magnetic fields along the $y$ direction are taken as an example. Three parameters (the purity of state $r$, the mixing angle $θ$ and the relative phase $β$) are chosen to characterize the initial states. The nodal points at which the usual geometric phases disappear are calculated and illustrated as a function of the three parameters.
We discuss a scheme for reconstructing experimentally the diagonal elements of the density matrix of quantum optical states. Applications to PDC heralded photons, multi-thermal and attenuated coherent states are illustrated and discussed in some details.
Noise avalanche and its quantum quenching in bosonic chains with random off-diagonal disorder
本文研究非对角无序玻色子链中光子数噪声的雪崩现象，发现经典相干激发导致超热聚束且无法淬灭，而单光子激发可有效阻止该雪崩。
Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity. Looking for states that have constant coherence under canonical changes of basis yields highly symmetric structures in state space. For the case of a qubit, we find an easy construction of qubit SICs (Symmetric Informationally Complete POVMs). SICs in dimension 3 and 8 are also shown to be equicoherent.
The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into two parts: one part where each basis vector undergoes cyclic evolution and one part where all basis …
Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis
本文提出基于重标度局域算符方差的可观测量无关可区分性度量，揭示 ETH 对角元与非对角元的普适权衡，并用 Ising 链数值结果统一子系统 ETH、弱 ETH 与宏观可观测量。
Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system have been investigated by means of a polarized neutron interferometer. Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.
Intramolecular singlet fission (iSF) materials provide remarkable advantages in terms of tunable electronic structures, and quantum chemistry studies have indicated strong electronic coupling modulation by high frequency phonon modes. In this work, we formulate a microscopic model of iSF with simultaneous diagonal and off-diagonal coupling to high-frequency modes. A non-perturbative treatment, the Dirac-Frenkel time-dependent variational approach is adopted using the multiple Davydov trial states. It is shown that both diagonal and off-diagonal coupling can aid efficient singlet fission if exc…
We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a fu…
Systems with purely off-diagonal disorder have peculiar features such as the localization-delocalization transition and long-range correlations in their wavefunctions. To motivate possible experimental studies of the physics of off-diagonal disorder, we study in detail disordered discrete-time quantum walk in a finite chain, where the diagonal disorder can be set to zero by construction. Starting from a transfer matrix approach, we show, both theoretically and computationally, that the dynamics of the quantum walk with disorder manifests all the main features of off-diagonal disorder. We also …
We investigate the adiabatic evolution of a set of non-degenerate eigenstates of a parameterized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.
We have carried out analytical and numerical studies of the spin-boson model in the sub-ohmic regime with the influence of both the diagonal and off-diagonal coupling accounted for via the Davydov D1 variational ansatz. While a second-order phase transition is known to be exhibited by this model in the presence of diagonal coupling only, we demonstrate the emergence of a discontinuous first order phase transition upon incorporation of the off-diagonal coupling. A plot of the ground state energy versus magnetization highlights the discontinuous nature of the transition between the isotropic (ze…
We analyze a one dimensional quantum model with off-diagonal disorder, consisting of a sequence of potential energy barriers whose width is a random variable either uniformly or normally distributed. We investigate how the disorder and the energy distribution (due to a thermostat at room temperature) affect the resulting value of the transmission coefficient, and discuss the structure of the fluctuations of such coefficient at different length scales and the onset of different size-dependent regimes. Our analysis suggests an efficient way to detect tunneling resonances in a regime of off-diago…
Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In literature, only diagonal heat kernels are calculated based on the covariant perturbation expansion.
We investigate a spin-boson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep sub-Ohmic regime there exists a novel second-order phase transition between two types of doubly degenerate states, which is reduced to one of the usual type for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.
By employing the variational approach, density matrix renormalization group (DMRG), exact diagonalization as well as symmetry and mean-field analyses, the ground state properties of the two-bath spin boson model with simultaneous diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic regime. A novel quantum phase transition from a doubly degenerate "localized phase" to the other doubly degenerate "delocalized phase" is uncovered. Via the multi-D1 ansatz as the variational wave function, transition points are determined accurately, consistent with the results from DMRG a…
Multitime system correlations functions are relevant in various areas of physics and science, dealing with system-bath interaction including spectroscopy and quantum optics, where many of these schemes include an off-diagonal system bath interaction. Here we extend the enhanced TEMPO algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett. 123, 240602 (2019)] to open quantum systems with off-diagonal coupling beyond a single two level system. We exemplify the approach on a coupled cavity waveguide system with spatially separated quantum two-state emitters, though many other…
Auxiliary dynamical mean-field approach for Anderson-Hubbard model with off-diagonal disorder
本研究提出ACPA-DMFT理论框架，统一处理对角与非对角无序并结合动力学平均场理论，计算了有限温简单立方晶格的格林函数与杂质谱函数，揭示非对角无序对莫特转变的关键影响及重入现象，为研究无序与强关联相互作用提供高效方法。
Improved results using a method similar to the Munn-Silbey approach have been obtained on the temperature dependence of transport properties of an extended Holstein model incorporating simultaneous diagonal and off-diagonal exciton-phonon coupling. The Hamiltonian is partially diagonalized by a canonical transformation, and optimal transformation coefficients are determined in a self-consistent manner. Calculated transport properties exhibit substantial corrections on those obtained previously by Munn and Silbey for a wide range of temperatures thanks to a numerically exact evaluation and an a…
No off-diagonal quantum focusing for Rényi divergences
研究量子聚焦猜想中关于Rényi散度的非对角部分，针对满足特定条件的Rényi型散度，通过相关证明对完整的Rényi聚焦表述是否成立这一问题给出否定答案。
The projected generator coordinate method based on the configuration mixing of non-orthogonal Bogoliubov product states, along with more advanced methods based on it, require the computation of off-diagonal Hamiltonian and norm kernels. While the Hamiltonian kernel is efficiently computed via the off-diagonal Wick theorem of Balian and Brezin, the norm kernel relies on the Onishi formula (or equivalently the Pfaffian formula by Robledo or the integral formula by Bally and Duguet). Traditionally, the derivation of these two categories of formulae rely on different formal schemes. In the present…
In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value, are all determined by the off-diagonal matrix elements. Motivated by this non-equilibrium role, we present generic statistical properties of off-diagonal matrix elements of local observables in two families o…
For a large class of quantum many-body systems with U(1) symmetry, we prove a general inequality that relates the (off-diagonal) long-range order with the charge gap. For a system of bosons or fermions on a lattice or in the continuum, the inequality implies that a ground state with off-diagonal long-range order inevitably has a vanishing charge gap, and hence is characterized by nonzero charge susceptibility. For a quantum spin system, the inequality implies that a ground state within a magnetization plateau cannot have transverse long-range order.
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