Unraveling the excitation spectrum of many-body systems from quantum quenches

Abstract

Quenches are now routinely used in synthetic quantum systems to study a variety of fundamental effects, including ergodicity breaking, light-cone-like spreading of information, and dynamical phase transitions. It was shown recently that the dynamics of equal-time correlators may be related to ground-state phase transitions and some properties of the system excitations. Here, we show that the full low-lying excitation spectrum of a generic many-body quantum system can be extracted from the after-quench dynamics of equal-time correlators. We demonstrate it for a variety of one-dimensional lattice models amenable to exact numerical calculations, including Bose and spin models, with short or long range interactions. The approach also applies to higher dimensions, correlated fermions, and continuous models. We argue that it provides an alternative approach to standard pump-probe spectroscopic methods and discuss its advantages.2E k J = 4 2 sin 2 (k/2) 2 sin 2 (k/2) +n U J ,

Finding the phase diagram of strongly correlated disordered bosons using quantum quenches

“…The use of the one-body correlator is motivated by the fact that it is known to be a suitable probe of the excitation spectrum of both MI and SF phases in the clean system [20], while the density was chosen as it is the simplest local probe which acts on only a single lattice site. Both are standard observables, readily measured in experiments: The density can be measured directly from quantum gas microscopes with single-site resolution, while g 1 (x, t) is the Fourier transform of the momentum distribution as measured by time-of-flight imaging.…”

“…For a two-point correlator such as g 1 (x, t), the main contribution to the QSF comes from the homogeneous term already present in the clean system [20] with an additional broadening of the observed signal due to the disorder, which we further discuss in Appendix B. An additional strong contribution close to k = 0 for frequencies ω > 0, caused by the sensitivity of the one-body correlator to the quasi-long-range order in the system, leads to a V-shaped continuum around k = 0.…”

“…New spectroscopic methods based on quantum quenches, known as quench spectroscopy, have recently emerged [18][19][20][21], where the initial 'pump' step is replaced by a weak quench which populates the low-lying excited states of the model. This quench can be either global [20] or local [21], and is highly flexible, allowing both for the system to generate its own excitations and for careful targeting of specific types of excitations [22].…”

“…New spectroscopic methods based on quantum quenches, known as quench spectroscopy, have recently emerged [18][19][20][21], where the initial 'pump' step is replaced by a weak quench which populates the low-lying excited states of the model. This quench can be either global [20] or local [21], and is highly flexible, allowing both for the system to generate its own excitations and for careful targeting of specific types of excitations [22]. In homogeneous systems, it has been demonstrated that spectral properties, including the dispersion relation of the elementary excitations, may then be obtained from the post-quench non-equilibrium dynamics via a straightforward Fourier transform [20,21].…”

“…This quench can be either global [20] or local [21], and is highly flexible, allowing both for the system to generate its own excitations and for careful targeting of specific types of excitations [22]. In homogeneous systems, it has been demonstrated that spectral properties, including the dispersion relation of the elementary excitations, may then be obtained from the post-quench non-equilibrium dynamics via a straightforward Fourier transform [20,21].…”