No Arabic abstract
An interferometric technique is proposed for determining the spatial forms of the individual degrees of freedom through which a many body system can absorb energy from its environment. The method separates out the coherent excitations present at any given frequency; it is not necessary to infer modal content from spectra. The system under test is excited with two external sources, which create generalized forces, and the fringe in the total power dissipated is measured as the relative phase between the sources is varied. If the complex fringe visibility is measured for different pairs of source locations, the anti-Hermitian part of the complex-valued non-local correlation tensor can be determined, which can then be decomposed to give the natural dynamical modes of the system and their relative responsivities. If each source in the interferometer creates a different kind of force, the spatial forms of the individual excitations that are responsible for cross-correlated response can be found. The technique is a generalization of holography because it measures the state of coherence to which the system is maximally sensitive. It can be applied across a wide range of wavelengths, in a variety of ways, to homogeneous media, thin films, patterned structures, and to components such as sensors, detectors and energy harvesting absorbers.
Time domain interferometry is a promising method to characterizes spatial and temporal correlations at x-ray energies, via the so-called intermediate scattering function and the related dynamical couple correlations. However, so far, it has only been analyzed for classical target systems. Here, we provide a quantum analysis, and suggest a scheme which allows to access quantum dynamical correlations. We further show how TDI can be used to exclude classical models for the target dynamics, and illustrate our results using a single particle in a double well potential.
Many quantum advantages in metrology and communication arise from interferometric phenomena. Such phenomena can occur on ultrafast time scales, particularly when energy-time entangled photons are employed. These have been relatively unexplored as their observation necessitates time resolution much shorter than conventional photon counters. Integrating nonlinear optical gating with conventional photon counters can overcome this limitation and enable subpicosecond time resolution. Here, using this technique and a Franson interferometer, we demonstrate high-visibility quantum interference with two entangled photons, where the one- and two-photon coherence times are both subpicosecond. We directly observe the spectral and temporal interference patterns, measure a visibility in the two-photon coincidence rate of $(85.3pm0.4)%$, and report a CHSH-Bell parameter of $2.42pm0.02$, violating the local-hidden variable bound by 21 standard deviations. The demonstration of energy-time entanglement with ultrafast interferometry provides opportunities for examining and exploiting entanglement in previously inaccessible regimes.
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semi-definiteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.
Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parameterized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parameterization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground state VQE. We apply the method to compute the single-particle Greens function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.
We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.