1
|
D'Onofrio M, Xie Y, Rasmusson AJ, Wolanski E, Cui J, Richerme P. Radial Two-Dimensional Ion Crystals in a Linear Paul Trap. PHYSICAL REVIEW LETTERS 2021; 127:020503. [PMID: 34296899 DOI: 10.1103/physrevlett.127.020503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
Collapse
Affiliation(s)
- Marissa D'Onofrio
- Indiana University Department of Physics, Bloomington, Indiana 47405, USA and Indiana University Quantum Science and Engineering Center, Bloomington, Indiana 47405, USA
| | - Yuanheng Xie
- Indiana University Department of Physics, Bloomington, Indiana 47405, USA and Indiana University Quantum Science and Engineering Center, Bloomington, Indiana 47405, USA
| | - A J Rasmusson
- Indiana University Department of Physics, Bloomington, Indiana 47405, USA and Indiana University Quantum Science and Engineering Center, Bloomington, Indiana 47405, USA
| | - Evangeline Wolanski
- Indiana University Department of Physics, Bloomington, Indiana 47405, USA and Indiana University Quantum Science and Engineering Center, Bloomington, Indiana 47405, USA
| | - Jiafeng Cui
- Indiana University Department of Physics, Bloomington, Indiana 47405, USA and Indiana University Quantum Science and Engineering Center, Bloomington, Indiana 47405, USA
| | - Philip Richerme
- Indiana University Department of Physics, Bloomington, Indiana 47405, USA and Indiana University Quantum Science and Engineering Center, Bloomington, Indiana 47405, USA
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Dessup T, Coste C, Saint Jean M. Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system. Phys Rev E 2016; 94:012217. [PMID: 27575133 DOI: 10.1103/physreve.94.012217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2016] [Indexed: 06/06/2023]
Abstract
We study the dynamics of localized nonlinear patterns in a quasi-one-dimensional many-particle system near a subcritical pitchfork bifurcation. The normal form at the bifurcation is given and we show that these patterns can be described as solitary-wave envelopes. They are stable in a large temperature range and can diffuse along the chain of interacting particles. During their displacements the particles are continually redistributed on the envelope. This change of particle location induces a small modulation of the potential energy of the system, with an amplitude that depends on the transverse confinement. At high temperature, this modulation is irrelevant and the thermal motion of the localized patterns displays all the characteristics of a free quasiparticle diffusion with a diffusion coefficient that may be deduced from the normal form. At low temperature, significant physical effects are induced by the modulated potential. In particular, the localized pattern may be trapped at very low temperature. We also exhibit a series of confinement values for which the modulation amplitudes vanishes. For these peculiar confinements, the mean-square displacement of the localized patterns also evidences free-diffusion behavior at low temperature.
Collapse
Affiliation(s)
- Tommy Dessup
- Laboratoire Matière et Systèmes Complexes, UMR No. 7057, CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire Matière et Systèmes Complexes, UMR No. 7057, CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire Matière et Systèmes Complexes, UMR No. 7057, CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| |
Collapse
|
4
|
Dessup T, Coste C, Saint Jean M. Hysteretic and intermittent regimes in the subcritical bifurcation of a quasi-one-dimensional system of interacting particles. Phys Rev E 2016; 93:012105. [PMID: 26871022 DOI: 10.1103/physreve.93.012105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Indexed: 11/07/2022]
Abstract
In this article, we study the effects of white Gaussian additive thermal noise on a subcritical pitchfork bifurcation. We consider a quasi-one-dimensional system of particles that are transversally confined, with short-range (non-Coulombic) interactions and periodic boundary conditions in the longitudinal direction. In such systems, there is a structural transition from a linear order to a staggered row, called the zigzag transition. There is a finite range of transverse confinement stiffnesses for which the stable configuration at zero temperature is a localized zigzag pattern surrounded by aligned particles, which evidences the subcriticality of the bifurcation. We show that these configurations remain stable for a wide temperature range. At zero temperature, the transition between a straight line and such localized zigzag patterns is hysteretic. We have studied the influence of thermal noise on the hysteresis loop. Its description is more difficult than at T=0 K since thermally activated jumps between the two configurations always occur and the system cannot stay forever in a unique metastable state. Two different regimes have to be considered according to the temperature value with respect to a critical temperature T_{c}(τ_{obs}) that depends on the observation time τ_{obs}. An hysteresis loop is still observed at low temperature, with a width that decreases as the temperature increases toward T_{c}(τ_{obs}). In contrast, for T>T_{c}(τ_{obs}) the memory of the initial condition is lost by stochastic jumps between the configurations. The study of the mean residence times in each configuration gives a unique opportunity to precisely determine the barrier height that separates the two configurations, without knowing the complete energy landscape of this many-body system. We also show how to reconstruct the hysteresis loop that would exist at T=0 K from high-temperature simulations.
Collapse
Affiliation(s)
- Tommy Dessup
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| |
Collapse
|
5
|
Yan LL, Wan W, Chen L, Zhou F, Gong SJ, Tong X, Feng M. Exploring structural phase transitions of ion crystals. Sci Rep 2016; 6:21547. [PMID: 26865229 PMCID: PMC4749997 DOI: 10.1038/srep21547] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Accepted: 01/27/2016] [Indexed: 11/09/2022] Open
Abstract
Phase transitions have been a research focus in many-body physics over past decades. Cold ions, under strong Coulomb repulsion, provide a repealing paradigm of exploring phase transitions in stable confinement by electromagnetic field. We demonstrate various conformations of up to sixteen laser-cooled (40)Ca(+) ion crystals in a home-built surface-electrode trap, where besides the usually mentioned structural phase transition from the linear to the zigzag, two additional phase transitions to more complicated two-dimensional configurations are identified. The experimental observation agrees well with the numerical simulation. Heating due to micromotion of the ions is analysed by comparison of the numerical simulation with the experimental observation. Our investigation implies very rich and complicated many-body behaviour in the trapped-ion systems and provides effective mechanism for further exploring quantum phase transitions and quantum information processing with ultracold trapped ions.
Collapse
Affiliation(s)
- L. L. Yan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - W. Wan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L. Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| | - F. Zhou
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| | - S. J. Gong
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - X. Tong
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| | - M. Feng
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
| |
Collapse
|
6
|
Moore J, Martin LL, Maayani S, Kim KH, Chandrahalim H, Eichenfield M, Martin IR, Carmon T. Regular oscillations and random motion of glass microspheres levitated by a single optical beam in air. OPTICS EXPRESS 2016; 24:2850-2857. [PMID: 26906853 DOI: 10.1364/oe.24.002850] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We experimentally report on optical binding of many glass particles in air that levitate in a single optical beam. A diversity of particle sizes and shapes interact at long range in a single Gaussian beam. Our system dynamics span from oscillatory to random and dimensionality ranges from 1 to 3D. The low loss for the center of mass motion of the beads could allow this system to serve as a standard many body testbed, similar to what is done today with atoms, but at the mesoscopic scale.
Collapse
|
7
|
Dessup T, Coste C, Saint Jean M. Subcriticality of the zigzag transition: A nonlinear bifurcation analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032917. [PMID: 25871182 DOI: 10.1103/physreve.91.032917] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Indexed: 06/04/2023]
Abstract
When repelling particles are confined by a transverse potential in quasi-one-dimensional geometry, the straight line equilibrium configuration becomes unstable at small confinement, in favor of a staggered row that may be inhomogeneous or homogeneous. This conformational phase transition is a pitchfork bifurcation called the zigzag transition. We study the zigzag transition in infinite and periodic finite systems with short-range interactions. We provide numerical evidence that in this case the bifurcation is subcritical since it exhibits phase coexistence and hysteretic behavior. The physical mechanism responsible for the change in the bifurcation character is the nonlinear coupling between the transverse soft mode at the transition and the longitudinal Goldstone mode linked to the translational or rotational invariance of the zigzag pattern. An asymptotic analysis, near the bifurcation threshold and assuming an infinite system, gives an explicit expression for the normal form of the bifurcation. We establish the subcriticality, and we describe with excellent precision the inhomogeneous zigzag patterns observed in the simulations. A direct test of the physical mechanism responsible for the bifurcation character evidences a quantitative agreement.
Collapse
Affiliation(s)
- Tommy Dessup
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| |
Collapse
|
8
|
Lemmer A, Cormick C, Schmiegelow CT, Schmidt-Kaler F, Plenio MB. Two-dimensional spectroscopy for the study of ion coulomb crystals. PHYSICAL REVIEW LETTERS 2015; 114:073001. [PMID: 25763956 DOI: 10.1103/physrevlett.114.073001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Indexed: 06/04/2023]
Abstract
Ion Coulomb crystals are currently establishing themselves as a highly controllable test bed for mesoscopic systems of statistical mechanics. The detailed experimental interrogation of the dynamics of these crystals, however, remains an experimental challenge. In this work, we show how to extend the concepts of multidimensional nonlinear spectroscopy to the study of the dynamics of ion Coulomb crystals. The scheme we present can be realized with state-of-the-art technology and gives direct access to the dynamics, revealing nonlinear couplings even in the presence of thermal excitations. We illustrate the advantages of our proposal showing how two-dimensional spectroscopy can be used to detect signatures of a structural phase transition of the ion crystal, as well as resonant energy exchange between modes. Furthermore, we demonstrate in these examples how different decoherence mechanisms can be identified.
Collapse
Affiliation(s)
- A Lemmer
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
| | - C Cormick
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
| | - C T Schmiegelow
- QUANTUM, Institut für Physik, Universität Mainz, D-55128 Mainz, Germany
| | - F Schmidt-Kaler
- QUANTUM, Institut für Physik, Universität Mainz, D-55128 Mainz, Germany
| | - M B Plenio
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
| |
Collapse
|
9
|
Observation of the Kibble–Zurek scaling law for defect formation in ion crystals. Nat Commun 2013; 4:2290. [DOI: 10.1038/ncomms3290] [Citation(s) in RCA: 193] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2013] [Accepted: 07/11/2013] [Indexed: 11/09/2022] Open
|
10
|
Mehta AC, Umrigar CJ, Meyer JS, Baranger HU. Zigzag phase transition in quantum wires. PHYSICAL REVIEW LETTERS 2013; 110:246802. [PMID: 25165952 DOI: 10.1103/physrevlett.110.246802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2013] [Indexed: 06/03/2023]
Abstract
We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.
Collapse
Affiliation(s)
- Abhijit C Mehta
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA
| | - C J Umrigar
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | - Julia S Meyer
- SPSMS, UMR-E 9001 CEA/UJF-Grenoble 1, INAC, Grenoble F-38054, France
| | - Harold U Baranger
- Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA
| |
Collapse
|
11
|
Kaufmann H, Ulm S, Jacob G, Poschinger U, Landa H, Retzker A, Plenio MB, Schmidt-Kaler F. Precise experimental investigation of eigenmodes in a planar ion crystal. PHYSICAL REVIEW LETTERS 2012; 109:263003. [PMID: 23368557 DOI: 10.1103/physrevlett.109.263003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2012] [Indexed: 06/01/2023]
Abstract
The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5×10(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.
Collapse
Affiliation(s)
- H Kaufmann
- QUANTUM, Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | | | | | | | | | | | | | | |
Collapse
|
12
|
Gong ZX, Lin GD, Duan LM. Temperature-driven structural phase transition for trapped ions and a proposal for its experimental detection. PHYSICAL REVIEW LETTERS 2010; 105:265703. [PMID: 21231680 DOI: 10.1103/physrevlett.105.265703] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Indexed: 05/30/2023]
Abstract
A Wigner crystal formed with trapped ions can undergo a structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be driven solely by a change in the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology.
Collapse
Affiliation(s)
- Zhe-Xuan Gong
- Department of Physics and MCTP, University of Michigan, Ann Arbor, Michigan 48109, USA
| | | | | |
Collapse
|
13
|
Crick DR, Ohadi H, Bhatti I, Thompson RC, Segal DM. Two-ion Coulomb crystals of Ca + in a Penning trap. OPTICS EXPRESS 2008; 16:2351-2362. [PMID: 18542313 DOI: 10.1364/oe.16.002351] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Results demonstrating laser cooling and observation of individual calcium ions in a Penning trap are presented. We show that we are able to trap, cool, image and manipulate the shape of very small ensembles of ions sufficiently well to produce two-ion 'Coulomb crystals' aligned along the magnetic field of a Penning trap. Images are presented which show the individual ions to be resolved in a two-ion crystal. A distinct change in the configuration of such a crystal is observed as the experimental parameters are changed. These structures could eventually be used as building blocks in a Penning trap based quantum computer.
Collapse
Affiliation(s)
- D R Crick
- Imperial College of Science, Technology and Medicine, Prince Consort Rd., London SW7 2AZ, UK
| | | | | | | | | |
Collapse
|
14
|
Zhu SL, Monroe C, Duan LM. Trapped ion quantum computation with transverse phonon modes. PHYSICAL REVIEW LETTERS 2006; 97:050505. [PMID: 17026088 DOI: 10.1103/physrevlett.97.050505] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2006] [Indexed: 05/12/2023]
Abstract
We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.
Collapse
Affiliation(s)
- Shi-Liang Zhu
- FOCUS Center and MCTP, Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
| | | | | |
Collapse
|
15
|
Morigi G, Fishman S. Dynamics of an ion chain in a harmonic potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066141. [PMID: 15697468 DOI: 10.1103/physreve.70.066141] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2004] [Revised: 10/26/2004] [Indexed: 05/24/2023]
Abstract
Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, and thus the eigenmodes are not phononic-like waves. We study chains of N>>1 ions and evaluate analytically the long-wavelength modes and the density of states in the short-wavelength limit. These results reproduce with good approximation the dynamics of chains consisting of dozens of ions. Moreover, they allow one to determine the critical transverse frequency required for the stability of the linear structure, which is found to be in agreement with results obtained by different theoretical methods [Phys. Rev. Lett. 71, 2753 (1993)]] and by numerical simulations [Phys. Rev. Lett. 70, 818 (1993)]]. We introduce and explore the thermodynamic limit for the ion chain. The thermodynamic functions are found to exhibit deviations from extensivity.
Collapse
Affiliation(s)
- Giovanna Morigi
- Department of Quantum Physics, University of Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | | |
Collapse
|
16
|
Morigi G, Fishman S. Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential. PHYSICAL REVIEW LETTERS 2004; 93:170602. [PMID: 15525060 DOI: 10.1103/physrevlett.93.170602] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2004] [Indexed: 05/24/2023]
Abstract
The density of ions trapped in a harmonic potential in one dimension is not uniform. Consequently the eigenmodes are not phononlike waves. We calculate the long-wavelength modes in the continuum limit, and evaluate the density of states in the short-wavelength limit for chains of N>>1 ions. Remarkably, the results that are found analytically in the thermodynamic limit provide a good estimate of the spectrum of excitations of small chains down to few tens of ions. The spectra are used to compute the thermodynamic functions of the chain. Deviations from the extensivity of the thermodynamic quantities are found. An analytic expression for the critical transverse frequency determining the stability of a linear chain is derived.
Collapse
Affiliation(s)
- Giovanna Morigi
- Department of Quantum Physics, University of Ulm, D-89069 Ulm, Germany
| | | |
Collapse
|
17
|
Course 5 Quantum information processing in ion traps I. ACTA ACUST UNITED AC 2004. [DOI: 10.1016/s0924-8099(03)80029-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
18
|
Course 6 Quantum information processing in ion traps II. ACTA ACUST UNITED AC 2004. [DOI: 10.1016/s0924-8099(03)80030-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|