Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR

Abstract

In the long quest to identify and compensate the sources of decoherence in many-body systems far from the ground state, the varied family of Loschmidt echoes (LEs) became an invaluable tool in several experimental techniques. A LE involves a time-reversal procedure to assess the effect of perturbations in a quantum excitation dynamics. However, when addressing macroscopic systems one is repeatedly confronted with limitations that seem insurmountable. This led to formulate the central hypothesis of irreversibility stating that the time-scale of decoherence, T3, is proportional to the time-scale of the many-body interactions we reversed, T2. We test this by implementing two experimental schemes based on Floquet Hamiltonians where the effective strength of the dipolar spinspin coupling, i.e. 1/T2, is reduced by a variable scale factor k. This extends the perturbations time scale, TΣ, in relation to T2. Strikingly, we observe the superposition of the normalized Loschmidt echoes for the bigger values of k. This manifests the dominance of the intrinsic dynamics over the perturbation factors, even when the Loschmidt echo is devised to reverse that intrinsic dynamics. Thus, in the limit where the reversible interactions dominate over perturbations, the LE decays within a time-scale, T3 ≈ T2/R with R = (0.15 ± 0.01), confirming the emergence of a perturbation independent regime. These results support the central hypothesis of irreversibility.

Learning quantum systems via out-of-time-order correlators

“…Specifically, motivated by recent advances in solid-state defects [32,33,39] and NMR [40][41][42], we focus on the scenario where an experimenter has state preparation and read-out capabilities over only a single "probe" qubit interacting with a larger system that one wishes to learn. We note that high-fidelity OTOC measurements have already been achieved in similar setups by using rapid global pulse sequences to reverse timeevolution [29,43,44]. Previous theoretical approaches to learning in this scenario have been limited to noninteracting dynamics [31,42,[45][46][47][48].…”

“…Our results thus highlight the potential gains that can be achieved by quantum experiments if they have sufficient control and coherence to apply time-reversed dynamics. Extraordinary experimental progress has led to an ever-increasing number of such platforms [27][28][29][30][57][58][59], and we envision that learning via OTOCs might find applications across these diverse physical contexts. Specific future directions include learning long-range cross-talk in quantum processors [60], and strongly-interacting problems in NMR [8].…”

“…(Importantly for our application, nearly all experimental techniques for time-reversal rely only on the type of interaction being reversed and require no knowledge of the specific Hamiltonian, which one might wish to learn. For example, the same pulse sequence reverses an arbitrary dipole-dipole coupling Hamiltonian in an NMR experiment [29].) Physically, the OTOC probes whether information encoded at site x at time zero is contained in correlations involving site x at time t. This is quantified by the squared commutator of a time-evolved operator at x with a local operator at…”

“…Physically, OTOCs quantify the spread of local quantum information into highly non-local, entangled correlations [26]. Experimental measurements of the OTOC typically employ reversed time-evolution to refocus these correlations, and have been performed on dozens of qubits in superconducting quantum processors and trapped ion quantum simulators, and hundreds of nuclear spins in NMR spectroscopy [27][28][29][30].…”

Loschmidt echo and Poincaré recurrences of entanglement

“…The studies of effects of Hamiltonian perturbations acting on the quantum evolution during the return path of time reversal have been extended in [18] and the decoherence effects for this Loschmidt echo have been analyzed in [19] with links to the Lyapunov exponent. Various interesting properties of Loschmidt echo have been studied by different groups being described in [20,21,22,23]. In the context of quantum computing the properties of fidelity and Loschmidt echo for time reversal were reported in [24,25].…”