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Tripathy D, Touil A, Gardas B, Deffner S. Quantum information scrambling in two-dimensional Bose-Hubbard lattices. CHAOS (WOODBURY, N.Y.) 2024; 34:043121. [PMID: 38579152 DOI: 10.1063/5.0199335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 03/22/2024] [Indexed: 04/07/2024]
Abstract
It is a well-understood fact that the transport of excitations throughout a lattice is intimately governed by the underlying structures. Hence, it is only natural to recognize that the dispersion of information also has to depend on the lattice geometry. In the present work, we demonstrate that two-dimensional lattices described by the Bose-Hubbard model exhibit information scrambling for systems as little as two hexagons. However, we also find that the out-of-time-ordered correlator (OTOC) shows the exponential decay characteristic for quantum chaos only for a judicious choice of local observables. More generally, the OTOC is better described by Gaussian-exponential convolutions, which alludes to the close similarity of information scrambling and decoherence theory.
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Affiliation(s)
- Devjyoti Tripathy
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Akram Touil
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Bartłomiej Gardas
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
- National Quantum Laboratory, College Park, Maryland 20740, USA
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2
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Martinez-Azcona P, Kundu A, Del Campo A, Chenu A. Stochastic Operator Variance: An Observable to Diagnose Noise and Scrambling. PHYSICAL REVIEW LETTERS 2023; 131:160202. [PMID: 37925720 DOI: 10.1103/physrevlett.131.160202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Revised: 07/21/2023] [Accepted: 09/11/2023] [Indexed: 11/07/2023]
Abstract
Noise is ubiquitous in nature, so it is essential to characterize its effects. Considering a fluctuating Hamiltonian, we introduce an observable, the stochastic operator variance (SOV), which measures the spread of different stochastic trajectories in the space of operators. The SOV obeys an uncertainty relation and allows us to find the initial state that minimizes the spread of these trajectories. We show that the dynamics of the SOV is intimately linked to that of out-of-time-order correlators, which define the quantum Lyapunov exponent λ. Our findings are illustrated analytically and numerically in a stochastic Lipkin-Meshkov-Glick Hamiltonian undergoing energy dephasing.
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Affiliation(s)
- Pablo Martinez-Azcona
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Aritra Kundu
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Adolfo Del Campo
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
- Donostia International Physics Center, E-20018 San Sebastián, Spain
| | - Aurélia Chenu
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
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3
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Li Z, Colombo S, Shu C, Velez G, Pilatowsky-Cameo S, Schmied R, Choi S, Lukin M, Pedrozo-Peñafiel E, Vuletić V. Improving metrology with quantum scrambling. Science 2023; 380:1381-1384. [PMID: 37384680 DOI: 10.1126/science.adg9500] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 05/19/2023] [Indexed: 07/01/2023]
Abstract
Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.
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Affiliation(s)
- Zeyang Li
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Simone Colombo
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chi Shu
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Gustavo Velez
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Saúl Pilatowsky-Cameo
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | - Soonwon Choi
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Mikhail Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Edwin Pedrozo-Peñafiel
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Vladan Vuletić
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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4
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Khalouf-Rivera J, Gamito J, Pérez-Bernal F, Arias JM, Pérez-Fernández P. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Dynamical aspects. Phys Rev E 2023; 107:064134. [PMID: 37464676 DOI: 10.1103/physreve.107.064134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito et al., Phys. Rev. E 106, 044125 (2022)2470-004510.1103/PhysRevE.106.044125]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.
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Affiliation(s)
- J Khalouf-Rivera
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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5
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Novotný J, Stránský P. Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator. Phys Rev E 2023; 107:054220. [PMID: 37329084 DOI: 10.1103/physreve.107.054220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Accepted: 05/09/2023] [Indexed: 06/18/2023]
Abstract
A detailed numerical study reveals that the asymptotic values of the standard-deviation-to-mean ratio of the out-of-time-ordered correlator in energy eigenstates can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely, the algebraic u(3) model, and demonstrate a clear correspondence between the energy-smoothed relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a chaos indicator.
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Affiliation(s)
- Jakub Novotný
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
| | - Pavel Stránský
- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
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Tunable itinerant spin dynamics with polar molecules. Nature 2023; 614:70-74. [PMID: 36725993 DOI: 10.1038/s41586-022-05479-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Accepted: 10/25/2022] [Indexed: 02/03/2023]
Abstract
Strongly interacting spins underlie many intriguing phenomena and applications1-4 ranging from magnetism to quantum information processing. Interacting spins combined with motion show exotic spin transport phenomena, such as superfluidity arising from pairing of spins induced by spin attraction5,6. To understand these complex phenomena, an interacting spin system with high controllability is desired. Quantum spin dynamics have been studied on different platforms with varying capabilities7-13. Here we demonstrate tunable itinerant spin dynamics enabled by dipolar interactions using a gas of potassium-rubidium molecules confined to two-dimensional planes, where a spin-1/2 system is encoded into the molecular rotational levels. The dipolar interaction gives rise to a shift of the rotational transition frequency and a collision-limited Ramsey contrast decay that emerges from the coupled spin and motion. Both the Ising and spin-exchange interactions are precisely tuned by varying the strength and orientation of an electric field, as well as the internal molecular state. This full tunability enables both static and dynamical control of the spin Hamiltonian, allowing reversal of the coherent spin dynamics. Our work establishes an interacting spin platform that allows for exploration of many-body spin dynamics and spin-motion physics using the strong, tunable dipolar interaction.
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