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arXiv:1910.06024 · Physical Review Research

Direct measurement of nonlocal interactions in the many-body localized phase

B. Chiaro, C. Neill, Annabelle Bohrdt, Michele Filippone, Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, R. Barends, Sergio Boixo, David A. Buell, Brian Burkett, Y. Chen, Z. Chen, Roberto Collins, A. Dunsworth, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Matthew P. Harrigan, Trent Huang, Sergei V. Isakov, Evan R. Jeffrey, Z. Jiang, Dvir Kafri, Kostyantyn Kechedzhi, J. Kelly, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Erik A. Lucero, Jarrod R. McClean, Xiao Mi, A. Megrant, Masoud Mohseni, J. Mutus, Matt McEwen, Ofer Naaman, M. Neeley, Murphy Yuezhen Niu, A. Petukhov, Chris Quintana, Nicholas C. Rubin, D. Sank, Kevin J. Satzinger, T. White, Z. Jamie Yao, P. Yeh, Adam Zalcman, Vadim Smelyanskiy, Hartmut Neven, Sarang Gopalakrishnan, Dmitry A. Abanin, Michael Knap, John M. Martinis, P. Roushan

Published Feb 22, 2022• 67 citations
arXivHTMLPDF

Abstract

The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase of matter. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modifications of the dynamics, rendering their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two-qubit density matrices allows us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here detect affirmative quantum correlations and exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.

DOI
10.1103/physrevresearch.4.013148

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The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase of matter. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modifications of the dynamics, rendering their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two-qubit density matrices allows us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here detect affirmative quantum correlations and exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.
In many-body localized (MBL) systems, entanglement propagates throughout the system despite the absence of transport. Early experiments have relied on population measurements to indirectly probe these entanglement dynamics. However, because the entanglement results from phase relationships between localized orbitals, it is more naturally probed with phase sensitive algorithms and measurement. In this thesis, we use an array of nearest neighbor coupled superconducting qubits to introduce phase sensitive protocols to the experimental study of MBL systems. We establish that system is MBL by demonstrating disorder induced ergodicity breaking and the presence of effective nonlocal interactions. We then use density matrix reconstructions to observe the hallmark slow growth of entanglement and provide a site-resolved spatial and temporal map of the developing entanglement. We also inspect the capacity of the MBL phase to preserve quantum correlations by observing the decay of distillable entanglement when Bell pair embedded in an MBL environment and dephased by remote excitation. In superconducting quantum processors, such as that used in the MBL study above, dissipation leads to computational errors and must be minimized. To that end, we also describe coherence engineering experiments in terms of the low power internal quality factor Qi of coplanar waveguide (CPW) resonators, a figure of merit characterizing dissipation in the quantum computing regime. We investigate titanium nitride as a superconducting base metal for quantum circuits. By optimizing the deposition conditions, we achieve a record low-power Qi in CPW resonators. We also characterize the dielectric loss due to flux trapping hole arrays. Since flux traps are commonly used to prevent magnetic vortex formation and dielectric loss is a limiting dissipation mechanism, it is important to estimate the contribution of flux traps to the dielectric dissipation budget. We find that for reasonable hole patterns the dielectric loss can be small while preventing vortex formation.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.
We are able to detect clear signatures of dephasing---a distinct trait of many-body localization (MBL)---via the dynamics of two-site entanglement, quantified through the concurrence. Using the protocol implemented by M. Schreiber et al. [Science 349, 842 (2015)], we show that in the MBL phase the average two-site entanglement decays in time as a power law, while in the Anderson localized phase it tends to a plateau. The power-law exponent is not universal and displays a clear dependence on the interaction strength. This behavior is also qualitatively different from the ergodic phase, where the two-site entanglement decays exponentially. All the results are obtained by means of time-dependent density matrix renormalization-group simulations and further corroborated by analytical calculations on an effective model. Two-site entanglement has been measured in cold atoms: our analysis paves the way for the first direct experimental test of many-body dephasing in the MBL phase.
Many-body localized (MBL) systems are characterized by the absence of transport and thermalization and, therefore, cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behavior of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly nonthermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behavior distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached) and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultracold atoms in disordered optical lattices, and the behavior of local observables provides a direct experimental signature of many-body localization.
Many-body localization (MBL) can occur when strong disorders prevent an interacting system from thermalization. To study the dynamics of such systems, performing an ensemble average over many different disorder configurations is typically necessary. Previous works have utilized an algorithm in which different disorder profiles are mapped into a quantum ancilla. By preparing the ancilla in a quantum superposition state, quantum parallelism can be harnessed to obtain the ensemble average in a single computation run. In this work, we modify this algorithm by performing a measurement on the ancilla. This enables the determination of conditional dynamics not only by the ensemble average but also by the quantum interference effect. Using a phenomenological analysis based on local integrals of motion, we demonstrate that this protocol can lead to an enhancement of the dephasing effect and a boost in entanglement growth for systems in the deep MBL phase. For a typical MBL system with short-range interactions, reaching saturation in entanglement usually takes an exponentially long time, which makes experimental explorations of long-time properties challenging. With our protocol, we demonstrate a significant reduction in the saturation time by several orders. This advancement facilitates easier access to the behavior in the long-time regime. We also present numerical simulations of the random XXZXXZXXZ model where this enhancement is also present in a smaller disorder strength, beyond the deep MBL regime.