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Kaufman B, Marquetand P, Rozgonyi T, Weinacht T. Long-Lived Electronic Coherences in Molecules. PHYSICAL REVIEW LETTERS 2023; 131:263202. [PMID: 38215370 DOI: 10.1103/physrevlett.131.263202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 09/29/2023] [Accepted: 11/01/2023] [Indexed: 01/14/2024]
Abstract
We demonstrate long-lived electronic coherences in molecules using a combination of measurements with shaped octave spanning ultrafast laser pulses and calculations of the light matter interaction. Our pump-probe measurements prepare and interrogate entangled nuclear-electronic wave packets whose electronic phase remains well defined despite vibrational motion along many degrees of freedom. The experiments and calculations illustrate how coherences between excited states can survive, even when coherence with the ground state is lost, and may have important implications for many areas of attosecond science and photochemistry.
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Affiliation(s)
- Brian Kaufman
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
| | - Philipp Marquetand
- University of Vienna, Faculty of Chemistry, Institute of Theoretical Chemistry, Währinger Strasse 17, 1090 Wien, Austria
| | - Tamás Rozgonyi
- Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
| | - Thomas Weinacht
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
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2
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Huang Z, Clerk A, Martin I. Nondispersing Wave Packets in Lattice Floquet Systems. PHYSICAL REVIEW LETTERS 2021; 126:100601. [PMID: 33784147 DOI: 10.1103/physrevlett.126.100601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Revised: 10/18/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
We show that in a one-dimensional translationally invariant tight binding chain, nondispersing wave packets can in general be realized as Floquet eigenstates-or linear combinations thereof-using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their "round-trip" time) locks in at rational ratios sT/r of the driving period T, where s, r are coprime integers. Wave packets of different s/r can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r=1) or over a long time (s/r≠1). Discrete time translation symmetry is manifestly broken for s≠1, reminiscent of integer and fractional Floquet time crystals. We further demonstrate how to reverse engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.
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Affiliation(s)
- Zhoushen Huang
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Aashish Clerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Ivar Martin
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
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Sacha K, Zakrzewski J. Time crystals: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:016401. [PMID: 28885193 DOI: 10.1088/1361-6633/aa8b38] [Citation(s) in RCA: 76] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals-the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek's idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.
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Affiliation(s)
- Krzysztof Sacha
- Instytut Fizyki imienia Mariana Smoluchowskiego and Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, ulica Profesora Stanisława Łojasiewicza, 11 PL-30-348 Kraków, Poland
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Yoshida S, Reinhold C, Burgdörfer J, Wyker B, Ye S, Dunning F. Analysis of circular wave packets generated by pulsed electric fields. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH. SECTION B, BEAM INTERACTIONS WITH MATERIALS AND ATOMS 2012; 279-222:4-7. [PMID: 23565015 PMCID: PMC3617732 DOI: 10.1016/j.nimb.2011.10.054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/22/2011] [Revised: 09/02/2011] [Indexed: 06/02/2023]
Abstract
We demonstrate that circular wave packets in high Rydberg states generated by a pulsed electric field applied to extreme Stark states are characterized by a position-dependent energy gradient that leads to a correlation between the principal quantum number n and the spatial coordinate. This correlation is rather insensitive to the initial state and can be seen even in an incoherent mix of states such as is generated experimentally allowing information to be placed into, and extracted from, such wave packets. We show that detailed information on the spatial distribution of a circular wave packet can be extracted by analyzing the complex phase of its expansion coefficients.
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Affiliation(s)
- S. Yoshida
- Institute for Theoretical Physics, Vienna University of Technology, Vienna, Austria
| | - C.O. Reinhold
- Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6372, USA
- Department of Physics, University of Tennessee, Knoxville, TN 37996, USA
| | - J. Burgdörfer
- Institute for Theoretical Physics, Vienna University of Technology, Vienna, Austria
- Department of Physics, University of Tennessee, Knoxville, TN 37996, USA
| | - B. Wyker
- Department of Physics and Astronomy and the Rice Quantum Institute, Rice University, Houston, TX 77005-1892, USA
| | - S. Ye
- Department of Physics and Astronomy and the Rice Quantum Institute, Rice University, Houston, TX 77005-1892, USA
| | - F.B. Dunning
- Department of Physics and Astronomy and the Rice Quantum Institute, Rice University, Houston, TX 77005-1892, USA
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Maeda H, Gurian JH, Gallagher TF. Nondispersing Bohr wave packets. PHYSICAL REVIEW LETTERS 2009; 102:103001. [PMID: 19392109 DOI: 10.1103/physrevlett.102.103001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2008] [Indexed: 05/27/2023]
Abstract
Long-lived, nondispersing circular, or Bohr, wave packets are produced starting from Li Rydberg atoms by exposing them first to a linearly polarized microwave field at the orbital frequency, 17.6 GHz at principal quantum number n=72, which locks the electron's motion into an approximately linear orbit in which the electron oscillates in phase with the microwave field. The microwave polarization is changed to circular polarization slowly compared to the orbital frequency, and the electron's motion follows, resulting in a nondispersing Bohr wave packet.
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Affiliation(s)
- H Maeda
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904-0714, USA
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Luan PG, Tang CS. Charged particle motion in a time-dependent flux-driven ring: an exactly solvable model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2007; 19:176224. [PMID: 21690969 DOI: 10.1088/0953-8984/19/17/176224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We consider a charged particle driven by a time-dependent flux threading a quantum ring. The dynamics of the charged particle is investigated using a classical treatment, a Fourier expansion technique, a time-evolution method, and the Lewis-Riesenfeld approach. We have shown that, by properly managing the boundary conditions, a time-dependent wavefunction can be obtained using a general non-Hermitian time-dependent invariant, which is a specific linear combination of initial angular-momentum and azimuthal-angle operators. It is shown that the linear invariant eigenfunction can be realized as a Gaussian-type wavepacket with a peak moving along the classical angular trajectory, while the distribution of the wavepacket is determined by the ratio of the coefficient of the initial angle to that of the initial canonical angular momentum. From the topologically nontrivial nature as well as the classical trajectory and angular momentum, one can determine the dynamical motion of the wavepacket. It should be noted that the peak position is no longer an expectation value of the angle operator, and hence the Ehrenfest theorem is not directly applicable in such a topologically nontrivial system.
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Affiliation(s)
- Pi-Gang Luan
- Department of Optics and Photonics, National Central University, Chung-Li 32054, Taiwan
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Shapiro EA, Walmsley IA, Ivanov MY. Suppression of decoherence in a wave packet via nonlinear resonance. PHYSICAL REVIEW LETTERS 2007; 98:050501. [PMID: 17358834 DOI: 10.1103/physrevlett.98.050501] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2005] [Revised: 09/18/2006] [Indexed: 05/14/2023]
Abstract
We propose a simple approach for suppressing decoherence of a wave packet excited in an anharmonic oscillator. We show that when a resonant external field forces the oscillator to follow the driving force, motion around the resonant trajectory inside a stable resonant island can be made almost completely immune to the environment. As an example, we study suppression of decoherence due to coupling to thermally populated rotations in vibrational wave packets in a Na2 molecule.
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Affiliation(s)
- E A Shapiro
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1
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Wimberger S, Schlagheck P, Eltschka C, Buchleitner A. Resonance-assisted decay of nondispersive wave packets. PHYSICAL REVIEW LETTERS 2006; 97:043001. [PMID: 16907569 DOI: 10.1103/physrevlett.97.043001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2006] [Indexed: 05/11/2023]
Abstract
We present a quantitative semiclassical theory for the decay of nondispersive electronic wave packets in driven, ionizing Rydberg systems. Statistically robust quantities are extracted combining resonance-assisted tunneling with subsequent transport across chaotic phase space and a final ionization step.
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Affiliation(s)
- Sandro Wimberger
- CNR-INFM and Dipartimento di Fisica E. Fermi, Unversità degli Studi di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
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Buchleitner A, d'Arcy MB, Fishman S, Gardiner SA, Guarneri I, Ma ZY, Rebuzzini L, Summy GS. Quantum accelerator modes from the Farey tree. PHYSICAL REVIEW LETTERS 2006; 96:164101. [PMID: 16712235 DOI: 10.1103/physrevlett.96.164101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2005] [Indexed: 05/09/2023]
Abstract
We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.
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Affiliation(s)
- A Buchleitner
- Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
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Stützle R, Göbel MC, Hörner T, Kierig E, Mourachko I, Oberthaler MK, Efremov MA, Fedorov MV, Yakovlev VP, van Leeuwen KAH, Schleich WP. Observation of nonspreading wave packets in an imaginary potential. PHYSICAL REVIEW LETTERS 2005; 95:110405. [PMID: 16196985 DOI: 10.1103/physrevlett.95.110405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2004] [Indexed: 05/04/2023]
Abstract
We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.
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Affiliation(s)
- R Stützle
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, D-69120 Heidelberg, Germany.
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11
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Kalinski M, Hansen L, Farrelly D. Nondispersive two-electron wave packets in a helium atom. PHYSICAL REVIEW LETTERS 2005; 95:103001. [PMID: 16196925 DOI: 10.1103/physrevlett.95.103001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2005] [Indexed: 05/04/2023]
Abstract
We demonstrate the existence of stable nondispersing two-electron wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum-dot helium with an impurity center.
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Affiliation(s)
- Matt Kalinski
- Department of Chemistry and Biochemistry, Utah State University, Logan, 84322-0300, USA
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Matulis A, Anisimovas E. A quasiclassical approach to strongly correlated quantum dots in intense magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2005; 17:3851-3864. [PMID: 21690702 DOI: 10.1088/0953-8984/17/25/012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We present a general quasiclassical description of parabolic many-electron quantum dots in the limit of high magnetic fields. The key points of our approach are the transition to a rotating frame of reference, in order to decouple rotational and vibrational modes, as well as the recognition and inclusion of the role of potential anisotropy felt by the vibrational modes. We are able to obtain the complete wavefunction of quantum dots containing any number of electrons in the Gaussian form, and present results concerning inter-particle correlation and deformation of large quantum dots.
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Affiliation(s)
- A Matulis
- Semiconductor Physics Institute, Goštauto 11, LT-01108 Vilnius, Lithuania
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13
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Maeda H, Norum DVL, Gallagher TF. Microwave Manipulation of an Atomic Electron in a Classical Orbit. Science 2005; 307:1757-60. [PMID: 15705805 DOI: 10.1126/science.1108470] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Although an atom is a manifestly quantum mechanical system, the electron in an atom can be made to move in a classical orbit almost indefinitely if it is exposed to a weak microwave field oscillating at its orbital frequency. The field effectively tethers the electron, phase-locking its motion to the oscillating microwave field. By exploiting this phase-locking, we have sped up or slowed down the orbital motion of the electron in excited lithium atoms by increasing or decreasing the microwave frequency between 13 and 19 gigahertz; the binding energy and orbital size change concurrently.
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Affiliation(s)
- H Maeda
- Department of Physics, University of Virginia, 382 McCormick Road, Charlottesville, VA 22904, USA.
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Carvalho ARR, Buchleitner A. Web-assisted tunneling in the kicked harmonic oscillator. PHYSICAL REVIEW LETTERS 2004; 93:204101. [PMID: 15600927 DOI: 10.1103/physrevlett.93.204101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2004] [Indexed: 05/24/2023]
Abstract
We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web states.
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Affiliation(s)
- André R R Carvalho
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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