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Dalla Torre EG, Reagor MJ. Simulating the Interplay of Particle Conservation and Long-Range Coherence. Phys Rev Lett 2023; 130:060403. [PMID: 36827580 DOI: 10.1103/physrevlett.130.060403] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 12/13/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
Lasers and Bose-Einstein condensates (BECs) exhibit macroscopic quantum coherence in seemingly unrelated ways. Lasers possess a well-defined global phase while the number of photons fluctuates. In BECs of atoms, instead, the number of particles is conserved and the global phase is undefined. Here, we use gate-based quantum circuits to create a unified framework that connects lasers and BEC states. Our approach relies on a scalable circuit that measures the total number of particles without destroying long-range coherence. We introduce two complementary probes of global and relative phase coherence, study how they are affected by measurements of the particle number, and implement them on a superconducting quantum computer by Rigetti. We find that particle conservation enhances long-range phase coherence, highlighting a mechanism used by superfluids and superconductors to gain phase stiffness.
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Affiliation(s)
- Emanuele G Dalla Torre
- Department of Physics and Center for Quantum Entanglement Science and Technology, Bar-Ilan University, 52900 Ramat Gan, Israel
- Superconducting Quantum Materials and Systems Center (SQMS), Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Matthew J Reagor
- Superconducting Quantum Materials and Systems Center (SQMS), Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Rigetti Computing, 775 Heinz Avenue, Berkeley, California 94710, USA
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Calvanese Strinati M, Bello L, Dalla Torre EG, Pe'er A. Can Nonlinear Parametric Oscillators Solve Random Ising Models? Phys Rev Lett 2021; 126:143901. [PMID: 33891458 DOI: 10.1103/physrevlett.126.143901] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 03/10/2021] [Indexed: 06/12/2023]
Abstract
We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is offered by the steady state of the network. This approach relies on the assumption that mode competition steers the network to the ground-state solution of the Ising model. By considering a broad family of frustrated Ising models, we show that the most efficient mode does not correspond generically to the ground state of the Ising model. We infer that networks of parametric oscillators close to threshold are intrinsically not Ising solvers. Nevertheless, the network can find the correct solution if the oscillators are driven sufficiently above threshold, in a regime where nonlinearities play a predominant role. We find that for all probed instances of the model, the network converges to the ground state of the Ising model with a finite probability.
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Affiliation(s)
- Marcello Calvanese Strinati
- Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
- Dipartimento di Fisica, Università di Roma "La Sapienza," Piazzale Aldo Moro 5, I-00185 Rome, Italy
| | - Leon Bello
- Department of Physics and QUEST Center of Quantum Science and Technology, Bar-Ilan University, 52900 Ramat-Gan, Israel
| | | | - Avi Pe'er
- Department of Physics and QUEST Center of Quantum Science and Technology, Bar-Ilan University, 52900 Ramat-Gan, Israel
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Azses D, Haenel R, Naveh Y, Raussendorf R, Sela E, Dalla Torre EG. Identification of Symmetry-Protected Topological States on Noisy Quantum Computers. Phys Rev Lett 2020; 125:120502. [PMID: 33016759 DOI: 10.1103/physrevlett.125.120502] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2020] [Accepted: 08/14/2020] [Indexed: 05/06/2023]
Abstract
Identifying topological properties is a major challenge because, by definition, topological states do not have a local order parameter. While a generic solution to this challenge is not available yet, a broad class of topological states, namely, symmetry-protected topological (SPT) states, can be identified by distinctive degeneracies in their entanglement spectrum. Here, we propose and realize two complementary protocols to probe these degeneracies based on, respectively, symmetry-resolved entanglement entropies and measurement-based computational algorithms. The two protocols link quantum information processing to the classification of SPT phases of matter. They invoke the creation of a cluster state and are implemented on an IBM quantum computer. The experimental findings are compared to noisy simulations, allowing us to study the stability of topological states to perturbations and noise.
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Affiliation(s)
- Daniel Azses
- Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel
- Center for Quantum Entanglement Science and Technology, Bar-Ilan University, Ramat Gan 5290002, Israel
| | - Rafael Haenel
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - Yehuda Naveh
- IBM Research-Haifa, Haifa University Campus, Mount Carmel, Haifa 31905, Israel
| | - Robert Raussendorf
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - Eran Sela
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Emanuele G Dalla Torre
- Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel
- Center for Quantum Entanglement Science and Technology, Bar-Ilan University, Ramat Gan 5290002, Israel
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Abstract
The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.
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Affiliation(s)
- Mor M. Roses
- Department of Physics, Bar-Ilan University, Ramat Gan, Israel
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Bello L, Calvanese Strinati M, Dalla Torre EG, Pe'er A. Persistent Coherent Beating in Coupled Parametric Oscillators. Phys Rev Lett 2019; 123:083901. [PMID: 31491203 DOI: 10.1103/physrevlett.123.083901] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Indexed: 06/10/2023]
Abstract
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network-two coupled parametric oscillators, where the oscillators never reach a steady state, but show persistent, full-scale, coherent beats, whose frequency reflects the coupling properties and strength. We present a detailed theoretical and experimental study and show that this new dynamical regime appears over a wide range of parameters near the oscillation threshold and depends on the nature of the coupling (dissipative or energy preserving). Thus, a system of coupled parametric oscillators transcends the Ising description and manifests unique coherent dynamics, which may have important implications for coherent computation machines.
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Affiliation(s)
- Leon Bello
- Department of Physics and BINA Center of Nanotechnology, Bar-Ilan University, 52900 Ramat-Gan, Israel
| | | | | | - Avi Pe'er
- Department of Physics and BINA Center of Nanotechnology, Bar-Ilan University, 52900 Ramat-Gan, Israel
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Affiliation(s)
- Mati Aharonyan
- Department of Physics and Center for Quantum Entanglement Science and Technology (QUEST), Bar-Ilan University, Ramat Gan, Israel
| | - Emanuele G. Dalla Torre
- Department of Physics and Center for Quantum Entanglement Science and Technology (QUEST), Bar-Ilan University, Ramat Gan, Israel
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Agarwal K, Dalla Torre EG, Rauer B, Langen T, Schmiedmayer J, Demler E. Chiral prethermalization in supersonically split condensates. Phys Rev Lett 2014; 113:190401. [PMID: 25415886 DOI: 10.1103/physrevlett.113.190401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2014] [Indexed: 06/04/2023]
Abstract
We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a supersonic unzipping of a single condensate. We use the Lorentz invariance of the low energy sector of such systems to show that dephasing results in an unusual prethermal state, in which right- and left-moving excitations have different, Doppler-shifted temperatures. The chirality of these modes can be probed experimentally by measuring the interference fringe contrasts with the release point of the split condensates moving at another supersonic velocity. Further, an accelerated motion of the release point can be used to observe a spacelike analog of the Unruh effect. A concrete experimental realization of the quantum zipper for a BEC of trapped atoms on an atom chip is outlined.
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Affiliation(s)
- Kartiek Agarwal
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | | | - Bernhard Rauer
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Tim Langen
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Jörg Schmiedmayer
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Eugene Demler
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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Abstract
We consider the dynamics of a Bose-Einstein condensate with two internal states, coupled through a coherent drive. We focus on a specific quench protocol, in which the sign of the coupling field is suddenly changed. At a mean-field level, the system is transferred from a minimum to a maximum of the coupling energy and can remain dynamically stable, in spite of the development of negative-frequency modes. In the presence of a nonzero detuning between the two states, the "charge" and "spin" modes couple, giving rise to an unstable avoided crossing. This phenomenon is generic to systems with two dispersing modes away from equilibrium and constitutes an example of class-I(o) nonequilibrium pattern formation in quantum systems.
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Affiliation(s)
- Nathan R Bernier
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Department of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
| | | | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 20138, USA
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Dalla Torre EG, Otterbach J, Demler E, Vuletic V, Lukin MD. Dissipative preparation of spin squeezed atomic ensembles in a steady state. Phys Rev Lett 2013; 110:120402. [PMID: 25166780 DOI: 10.1103/physrevlett.110.120402] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2012] [Revised: 12/21/2012] [Indexed: 06/03/2023]
Abstract
We present and analyze a new approach for the generation of atomic spin-squeezed states. Our method involves the collective coupling of an atomic ensemble to a decaying mode of an open optical cavity. We demonstrate the existence of a collective atomic dark state, decoupled from the radiation field. By explicitly constructing this state we find that it can feature spin squeezing bounded only by the Heisenberg limit. We show that such dark states can be deterministically prepared via dissipative means, thus turning dissipation into a resource for entanglement. The scaling of the phase sensitivity taking realistic imperfections into account is discussed.
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Affiliation(s)
| | - Johannes Otterbach
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Eugene Demler
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Vladan Vuletic
- Physics Department, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mikhail D Lukin
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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Dalla Torre EG, Demler E, Polkovnikov A. Universal rephasing dynamics after a quantum quench via sudden coupling of two initially independent condensates. Phys Rev Lett 2013; 110:090404. [PMID: 23496694 DOI: 10.1103/physrevlett.110.090404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 06/01/2023]
Abstract
We consider a quantum quench in which two initially independent condensates are suddenly coupled and study the subsequent "rephasing" dynamics. For weak tunneling couplings, the time evolution of physical observables is predicted to follow universal scaling laws, connecting the short-time dynamics to the long-time nonperturbative regime. We first present a two-mode model valid in two and three dimensions and then move to one dimension, where the problem is described by a gapped sine-Gordon theory. Combining analytical and numerical methods, we compute universal time-dependent expectation values, allowing a quantitative comparison with future experiments.
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Abstract
We investigate the phase diagram of spinless bosons with long range (variant 1/r(3)) repulsive interactions, relevant to ultracold polarized atoms or molecules, using density matrix renormalization group. Between the two conventional insulating phases, the Mott and density wave phases, we find a new phase possessing hidden order revealed by nonlocal string correlations analogous to those characterizing the Haldane gapped phase of integer spin chains. We develop a mean field theory that describes the low-energy excitations in all three insulating phases. This is used to calculate the absorption spectrum due to oscillatory lattice modulation. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase.
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Affiliation(s)
- Emanuele G Dalla Torre
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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