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Duca L, Mizukami N, Perego E, Inguscio M, Sias C. Orientational Melting in a Mesoscopic System of Charged Particles. PHYSICAL REVIEW LETTERS 2023; 131:083602. [PMID: 37683173 DOI: 10.1103/physrevlett.131.083602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 03/04/2023] [Accepted: 07/17/2023] [Indexed: 09/10/2023]
Abstract
A mesoscopic system of a few particles can undergo changes of configuration that resemble phase transitions but with a nonuniversal behavior. A notable example is orientational melting, in which localized particles with long-range repulsive interactions forming a two-dimensional crystal become delocalized in common closed trajectories. Here we report the observation of orientational melting occurring in a two-dimensional crystal of up to 15 ions. We measure density-density correlations to quantitatively characterize the occurrence of melting, and use a Monte Carlo simulation to extract the angular kinetic energy of the ions. By adding a pinning impurity, we demonstrate the nonuniversality of orientational melting and create novel configurations in which localized and delocalized particles coexist. Our system realizes an experimental testbed for studying changes of configurations in two-dimensional mesoscopic systems, and our results pave the way for the study of quantum phenomena in ensembles of delocalized ions.
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Affiliation(s)
- Lucia Duca
- Istituto Nazionale di Ricerca Metrologica (INRiM), 10135 Torino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
| | - Naoto Mizukami
- Istituto Nazionale di Ricerca Metrologica (INRiM), 10135 Torino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Politecnico di Torino, 10129 Torino, Italy
| | - Elia Perego
- Istituto Nazionale di Ricerca Metrologica (INRiM), 10135 Torino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
| | - Massimo Inguscio
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Carlo Sias
- Istituto Nazionale di Ricerca Metrologica (INRiM), 10135 Torino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
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Hutzler S, Ryan-Purcell J, Mughal A, Weaire D. A continuum description of the buckling of a line of spheres in a transverse harmonic confining potential. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230293. [PMID: 37448480 PMCID: PMC10336375 DOI: 10.1098/rsos.230293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 06/22/2023] [Indexed: 07/15/2023]
Abstract
A line of contacting hard spheres, placed in a transverse confining potential, buckles under compression or when tilted away from the horizontal, once a critical tilt angle is exceeded. This interesting nonlinear problem is enriched by the combined application of both compression and tilt. In a continuous formulation, the profile of transverse sphere displacement is well described by numerical solutions of a second-order differential equation (provided that buckling is not of large amplitude). Here we provide a detailed discussion of these solutions, which are approximated by analytic expressions in terms of Jacobi, Whittaker and Airy functions. The analysis in terms of Whittaker functions yields an exact result for the critical tilt for buckling without compression.
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Affiliation(s)
- S. Hutzler
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Republic of Ireland
| | - J. Ryan-Purcell
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Republic of Ireland
| | - A. Mughal
- Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales SY23 3BZ, UK
| | - D. Weaire
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Republic of Ireland
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S BK, Huse DA, Kulkarni M. Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators. Phys Rev E 2021; 104:044117. [PMID: 34781511 DOI: 10.1103/physreve.104.044117] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Accepted: 09/23/2021] [Indexed: 11/07/2022]
Abstract
We present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝∑_{i,j=1(i≠j)}^{N}|x_{i}-x_{j}|^{-k}∀k>1 where x_{i} is the position of the ith particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the "light cone." We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1<k<3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.
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Affiliation(s)
- Bhanu Kiran S
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - David A Huse
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Manas Kulkarni
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
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Kumar A, Kulkarni M, Kundu A. Particles confined in arbitrary potentials with a class of finite-range repulsive interactions. Phys Rev E 2020; 102:032128. [PMID: 33076043 DOI: 10.1103/physreve.102.032128] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2019] [Accepted: 08/19/2020] [Indexed: 11/07/2022]
Abstract
In this paper, we develop a large N field theory for a system of N classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, V_{ex}(x), and repel each other via a class of pairwise interaction potentials V_{int}(r) (where r is distance between a pair of particles) such that V_{int}∼|r|^{-k} when r→0. We consider the case where every particle is interacting with d (finite-range parameter) number of particles to its left and right. Due to the intricate interplay between external confinement, pairwise repulsion, and entropy, the density exhibits markedly distinct behavior in three regimes k>0, k→0, and k<0. From this field theory, we compute analytically the average density profile for large N in these regimes. We show that the contribution from interaction dominates the collective behavior for k>0 and the entropy contribution dominates for k<0, and both contribute equivalently in the k→0 limit (finite-range log-gas). Given the fact that this family of systems is of broad relevance, our analytical findings are of paramount importance. These results are in excellent agreement with brute-force Monte Carlo simulations.
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Affiliation(s)
- Avanish Kumar
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Manas Kulkarni
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Anupam Kundu
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
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Gambetta FM, Zhang C, Hennrich M, Lesanovsky I, Li W. Long-Range Multibody Interactions and Three-Body Antiblockade in a Trapped Rydberg Ion Chain. PHYSICAL REVIEW LETTERS 2020; 125:133602. [PMID: 33034467 DOI: 10.1103/physrevlett.125.133602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 08/27/2020] [Indexed: 06/11/2023]
Abstract
Trapped Rydberg ions represent a flexible platform for quantum simulation and information processing that combines a high degree of control over electronic and vibrational degrees of freedom. The possibility to individually excite ions to high-lying Rydberg levels provides a system where strong interactions between pairs of excited ions can be engineered and tuned via external laser fields. We show that the coupling between Rydberg pair interactions and collective motional modes gives rise to effective long-range and multibody interactions consisting of two, three, and four-body terms. Their shape, strength, and range can be controlled via the ion trap parameters and strongly depends on both the equilibrium configuration and vibrational modes of the ion crystal. By focusing on an experimentally feasible quasi one-dimensional setup of ^{88}Sr^{+} Rydberg ions, we demonstrate that multibody interactions are enhanced by the emergence of soft modes associated with, e.g., a structural phase transition. This has a striking impact on many-body electronic states and results-for example-in a three-body antiblockade effect that can be employed as a sensitive probe to detect structural phase transitions in Rydberg ion chains. Our study unveils the possibilities offered by trapped Rydberg ions for studying exotic phases of matter and quantum dynamics driven by enhanced multibody interactions.
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Affiliation(s)
- Filippo M Gambetta
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Chi Zhang
- Department of Physics, Stockholm University, 10691 Stockholm, Sweden
| | - Markus Hennrich
- Department of Physics, Stockholm University, 10691 Stockholm, Sweden
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Institut für Theoretische Physik, University of Tübingen, 72076 Tübingen, Germany
| | - Weibin Li
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Hutzler S, Mughal A, Ryan-Purcell J, Irannezhad A, Weaire D. Buckling of a linear chain of hard spheres in a harmonic confining potential: Numerical and analytical results for low and high compression. Phys Rev E 2020; 102:022905. [PMID: 32942376 DOI: 10.1103/physreve.102.022905] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 07/24/2020] [Indexed: 11/07/2022]
Abstract
We extend a previous analysis of the buckling properties of a linear chain of hard spheres between hard walls under transverse harmonic confinement. Two regimes are distinguished-low compression, for which the entire chain buckles, and higher compression, for which there is localized buckling. With further increase of compression, second-neighbor contacts occur; beyond this compression the structure is no longer planar, and is not treated here. A continuous model is developed which is amenable to analytical solution in the low compression regime. This is helpful in understanding the scaling properties of both finite and infinite chains.
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Affiliation(s)
- Stefan Hutzler
- School of Physics, Trinity College Dublin, Dublin 2, D02 PN40 Ireland
| | - Adil Mughal
- Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales SY23, United Kingdom
| | - John Ryan-Purcell
- School of Physics, Trinity College Dublin, Dublin 2, D02 PN40 Ireland
| | - Ali Irannezhad
- School of Physics, Trinity College Dublin, Dublin 2, D02 PN40 Ireland
| | - Denis Weaire
- School of Physics, Trinity College Dublin, Dublin 2, D02 PN40 Ireland
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Ruiz-García A, Alonso D. Spatial configurations and temperature profiles in nonequilibrium steady state of two-species trapped ion systems. Phys Rev E 2020; 101:012129. [PMID: 32069590 DOI: 10.1103/physreve.101.012129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Indexed: 11/07/2022]
Abstract
We study Coulomb crystals containing two ion species simultaneously confined in radio frequency traps and coupled to different thermal reservoirs located in two separate regions. We use a three-dimensional model to simulate the trapped bicrystal and show in a numerically rigorous manner the effects of the mass dependence of the trapping frequencies on the underlying nonequilibrium dynamics and the temperature profiles. By solving the classical Langevin equations of motion, we obtain the spatial probability densities of the two ion species and the kinetic temperature profiles across the axial direction of the trap in the nonequilibrium steady state. We analyze trapping conditions leading to bicrystals that exhibit ion conformations ranging from a linear chain of alternating ion species to two- and three-dimensional configurations. The results evidence the spatial segregation of the two ion species due to the mass dependence of the trapping frequencies and the increase of ion delocalization for heavier ion species and/or weaker trapping confinements. We also show the correlation between the increase of the temperature gradient in the bulk and this enhancement of ion delocalization through the trap.
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Affiliation(s)
- A Ruiz-García
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain and IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
| | - D Alonso
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain and IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
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Ruiz-García A, Fernández JJ, Alonso D. Delocalization and heat transport in multidimensional trapped ion systems. Phys Rev E 2019; 99:062105. [PMID: 31330614 DOI: 10.1103/physreve.99.062105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2019] [Indexed: 11/07/2022]
Abstract
We study the connection between heat transport properties of systems coupled to different thermal baths in two separate regions and their underlying nonequilibrium dynamics. We consider classical systems of interacting particles that may exhibit a certain degree of delocalization and whose effective dimensionality can be modified through the controlled variation of a global trapping potential. We focus on Coulomb crystals of trapped ions, which offer a versatile playground to shed light on the role that spatial constraints play on heat transport. We use a three-dimensional model to simulate the trapped ion system and show in a numerically rigorous manner to what extent heat transport properties could be feasibly tuned across the structural phase transitions among the linear, planar zigzag, and helical configurations. By solving the classical Langevin equations of motion, we analyze the steady state spatial distributions of the particles, the temperature profiles, and total heat flux through the various structural phase transitions that the system may experience. The results evidence a clear correlation between the degree of delocalization of the internal ions and the emergence of a nonzero gradient in the temperature profiles. The signatures of the phase transitions in the total heat flux as well as the optimal spatial configuration for heat transport are shown.
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Affiliation(s)
- A Ruiz-García
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain.,IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
| | - J J Fernández
- Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, United Kingdom
| | - D Alonso
- Departamento de Física, Universidad de La Laguna, La Laguna 38203, Spain.,IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain
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