Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System

Abstract

Evaluating the role of perturbations versus the intrinsic coherent dynamics in driving to equilibrium is of fundamental interest to understand quantum many-body thermalization, in the quest to build ever complex quantum devices. Here we introduce a protocol that scales down the coupling strength in a quantum simulator based on a solid-state nuclear spin system, leading to a longer decay time T2, while keeping perturbations associated to control error constant. We can monitor quantum information scrambling by measuring two powerful metrics, out-of-time-ordered correlators (OTOCs) and Loschmidt Echoes (LEs). While OTOCs reveal quantum information scrambling involving hundreds of spins, the LE decay quantifies, via the time scale T3, how well the scrambled information can be recovered through time reversal. We find that when the interactions dominate the perturbation, the LE decay rate only depends on the interactions themselves, T3 ∝ T2, and not on the perturbation. Then, in an unbounded many-spin system, decoherence can achieve a perturbation-independent regime, with a rate only related to the local second moment of the Hamiltonian.

Decoherence scaling transition in the dynamics of quantum information scrambling

“…Loschmidt echoes and MQC evince out-of-time order correlations (OTOC) [4,6], as they measure the scrambling of the information over a large system from an initially localized state [27,28,33]. They are therefore promising tools for finding answers to open questions related to quantum chaos [34][35][36], irreversibility [33,37], thermalization [38], and entanglement [28]. Hence, these OTOCs trigger a broad interest in diverse fields of physics, such as condensed matter and quantum gravity [27,28,35,36,[38][39][40][41], opening avenues for understanding the dynamics of quantum information in complex systems [4,6].…”

How many particles make up a chaotic many-body quantum system?

“…Quantum chaos, especially when caused by particle interactions, has seen a revival in the last decade or so, because it is closely related with topics of high experimental and theoretical in-terest. It is behind the mechanism of thermalization of isolated many-body quantum systems and the validity of the eigenstate thermalization hypothesis (ETH) [1][2][3], it explains the heating of driven systems [4,5], it is the main obstacle for many-body localization [6][7][8][9], it inhibits long-time simulation of many-body quantum systems [10], it can lead to the fast scrambling of quantum information [11], and it is the regime where the phenomenon of quantum scarring may be observed [12][13][14].…”

Information Scrambling and Loschmidt Echo

“…In particular, in spite of the absence of the tell-tale exponential sensitivity to initial conditions in unitary quantum evolution, one can use as a quantum diagnostic of chaos sensitivity of the evolution to small perturbations of the Hamiltonian [3] or its entropy production in presence of the coupling to the environment [4,5]. These and related manifestations of quantum chaos have been by now intensively studied [6][7][8][9][10][11][12][13], using phenomena such as Loschmidt echo (LE) [14,15],…”

“…For instance, when A and B are chosen as unitary operators, Eq. (2) can be directly measured by echo experiments [13,[40][41][42][43]. There are efforts to build more direct links between these two quantities, e.g., using variants of the OTOC and LE, or particular choices of operators for the OTOC evaluation [44][45][46].…”