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Tutunnikov I, Chuang C, Cao J. Coherent Spatial Control of Wave Packet Dynamics on Quantum Lattices. J Phys Chem Lett 2023; 14:11632-11639. [PMID: 38100722 DOI: 10.1021/acs.jpclett.3c03047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2023]
Abstract
Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.
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Affiliation(s)
- Ilia Tutunnikov
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Chern Chuang
- Department of Chemistry and Biochemistry, University of Nevada, 4505 S Maryland Pkwy, Las Vegas, Nevada 89154, United States
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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Abstract
We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.
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Cuadra L, Nieto-Borge JC. Approaching Disordered Quantum Dot Systems by Complex Networks with Spatial and Physical-Based Constraints. NANOMATERIALS 2021; 11:nano11082056. [PMID: 34443887 PMCID: PMC8400585 DOI: 10.3390/nano11082056] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Revised: 07/22/2021] [Accepted: 08/03/2021] [Indexed: 01/01/2023]
Abstract
This paper focuses on modeling a disordered system of quantum dots (QDs) by using complex networks with spatial and physical-based constraints. The first constraint is that, although QDs (=nodes) are randomly distributed in a metric space, they have to fulfill the condition that there is a minimum inter-dot distance that cannot be violated (to minimize electron localization). The second constraint arises from our process of weighted link formation, which is consistent with the laws of quantum physics and statistics: it not only takes into account the overlap integrals but also Boltzmann factors to include the fact that an electron can hop from one QD to another with a different energy level. Boltzmann factors and coherence naturally arise from the Lindblad master equation. The weighted adjacency matrix leads to a Laplacian matrix and a time evolution operator that allows the computation of the electron probability distribution and quantum transport efficiency. The results suggest that there is an optimal inter-dot distance that helps reduce electron localization in QD clusters and make the wave function better extended. As a potential application, we provide recommendations for improving QD intermediate-band solar cells.
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Affiliation(s)
- Lucas Cuadra
- Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
- Correspondence:
| | - José Carlos Nieto-Borge
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
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Cuadra L, Nieto-Borge JC. Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links. NANOMATERIALS (BASEL, SWITZERLAND) 2021; 11:375. [PMID: 33540687 PMCID: PMC7912992 DOI: 10.3390/nano11020375] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 01/18/2021] [Accepted: 01/27/2021] [Indexed: 12/28/2022]
Abstract
This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected.
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Affiliation(s)
- Lucas Cuadra
- Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
| | - José Carlos Nieto-Borge
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
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Xiong D, Thiel F, Barkai E. Using Hilbert transform and classical chains to simulate quantum walks. Phys Rev E 2017; 96:022114. [PMID: 28950452 DOI: 10.1103/physreve.96.022114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Indexed: 06/07/2023]
Abstract
We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such a wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Felix Thiel
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
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Cedzich C, Rybár T, Werner AH, Alberti A, Genske M, Werner RF. Propagation of quantum walks in electric fields. PHYSICAL REVIEW LETTERS 2013; 111:160601. [PMID: 24182244 DOI: 10.1103/physrevlett.111.160601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Indexed: 06/02/2023]
Abstract
We study one-dimensional quantum walks in a homogenous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion, and Anderson localization, depend very sensitively on the value of the electric field, Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.
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Affiliation(s)
- C Cedzich
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
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Mülken O, Bauer M. Directed excitation transfer in vibrating chains by external fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061123. [PMID: 21797318 DOI: 10.1103/physreve.83.061123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2010] [Revised: 03/03/2011] [Indexed: 05/31/2023]
Abstract
We study the coherent dynamics of excitations on vibrating chains. By applying an external field and matching the field strength with the oscillation frequency of the chain it is possible to obtain an (average) transport of an initial Gaussian wave packet. We distinguish between a uniform oscillation of all nodes of the chain and the chain being in its lowest eigenmode. Both cases can lead to directed transport.
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Affiliation(s)
- Oliver Mülken
- Physikalisches Institut, Universität Freiburg, Freiburg, Germany
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Abstract
This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.
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Affiliation(s)
- Kenji Ohmori
- Institute for Molecular Science, National Institutes of Natural Sciences; The Graduate University for Advanced Studies (SOKENDAI); and CREST, Japan Science and Technology Agency, Myodaiji, Okazaki 444-8585, Japan
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Xu XP, Li W, Liu F. Coherent transport on Apollonian networks and continuous-time quantum walks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:052103. [PMID: 19113175 DOI: 10.1103/physreve.78.052103] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2008] [Indexed: 05/27/2023]
Abstract
We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.
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Affiliation(s)
- Xin-Ping Xu
- Institute of Particle Physics, HuaZhong Normal University, Wuhan 430079, China
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Xu XP. Continuous-time quantum walks on one-dimensional regular networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061127. [PMID: 18643237 DOI: 10.1103/physreve.77.061127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2007] [Revised: 03/24/2008] [Indexed: 05/26/2023]
Abstract
In this paper, we consider continuous-time quantum walks (CTQWs) on a one-dimensional ring lattice of N nodes in which every node is connected to its 2m nearest neighbors ( m on either side). In the framework of the Bloch function ansatz, we calculate the space-time transition probabilities between two nodes of the lattice. We find that the transport of CTQWs between two different nodes is faster than that of the classical continuous-time random walks (CTRWs). The transport speed, which is defined by the ratio of the shortest path length and propagating time, increases with the connectivity parameter m for both CTQWs and CTRWs. For fixed parameter m , the transport of CTRWs gets slower with the increase of the shortest distance while the transport (speed) of CTQWs turns out to be a constant value. In the long-time limit, depending on the network size N and connectivity parameter m , the limiting probability distributions of CTQWs show various patterns. When the network size N is an even number, the probability of being at the original node differs from that of being at the opposite node, which also depends on the precise value of parameter m .
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Affiliation(s)
- Xin-Ping Xu
- Institute of Particle Physics, HuaZhong Normal University, Wuhan 430079, China.
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Perets HB, Lahini Y, Pozzi F, Sorel M, Morandotti R, Silberberg Y. Realization of quantum walks with negligible decoherence in waveguide lattices. PHYSICAL REVIEW LETTERS 2008; 100:170506. [PMID: 18518267 DOI: 10.1103/physrevlett.100.170506] [Citation(s) in RCA: 94] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2007] [Indexed: 05/26/2023]
Abstract
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially an implementation of quantum walks. Since waveguide lattices are easily constructed at large scales and display negligible decoherence, they can serve as an ideal and versatile experimental playground for the study of quantum walks and quantum algorithms. We experimentally observe quantum walks in large systems ( approximately 100 sites) and confirm quantum walks effects which were studied theoretically, including ballistic propagation, disorder, and boundary related effects.
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Affiliation(s)
- Hagai B Perets
- Faculty of Physics, The Weizmann Institute of Science, 76100 Rehovot, Israel.
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Mülken O, Pernice V, Blumen A. Quantum transport on small-world networks: a continuous-time quantum walk approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051125. [PMID: 18233641 DOI: 10.1103/physreve.76.051125] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2007] [Revised: 07/31/2007] [Indexed: 05/25/2023]
Abstract
We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWNs). The SWNs are built from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks, and we evaluate numerically the ensemble-averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWNs is, first, very fast, given that the limiting value of the transition probability is reached very quickly, and second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.
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Affiliation(s)
- Oliver Mülken
- Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany.
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Mülken O, Blumen A, Amthor T, Giese C, Reetz-Lamour M, Weidemüller M. Survival probabilities in coherent exciton transfer with trapping. PHYSICAL REVIEW LETTERS 2007; 99:090601. [PMID: 17930996 DOI: 10.1103/physrevlett.99.090601] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2007] [Indexed: 05/25/2023]
Abstract
In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the Hamiltonian. For linear systems and at intermediate times the decay obeys a power law, in contrast with the corresponding exponential decay found in incoherent continuous-time random walk situations. To differentiate between the coherent and incoherent mechanisms, we present an experimental protocol based on a frozen Rydberg gas structured by optical dipole traps.
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Affiliation(s)
- Oliver Mülken
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg i.Br., Germany
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Mülken O, Bierbaum V, Blumen A. Localization of coherent exciton transport in phase space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:031121. [PMID: 17500682 DOI: 10.1103/physreve.75.031121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2006] [Revised: 01/31/2007] [Indexed: 05/15/2023]
Abstract
We study numerically the dynamics of excitons on discrete rings in the presence of static disorder. Based on continuous-time quantum walks we compute the time evolution of the Wigner function (WF) both for pure diagonal (site) disorder, as well as for diagonal and off-diagonal (site and transfer) disorder. In both cases, large disorder leads to localization and destroys the characteristic phase space patterns of the WF found in the absence of disorder.
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Affiliation(s)
- Oliver Mülken
- Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
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Mülken O, Blumen A. Efficiency of quantum and classical transport on graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066117. [PMID: 16906924 DOI: 10.1103/physreve.73.066117] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2006] [Indexed: 05/11/2023]
Abstract
We propose a measure to quantify the efficiency of classical and quantum mechanical transport processes on graphs. The measure only depends on the density of states (DOS), which contains all the necessary information about the graph. For some given (continuous) DOS, the measure shows a power law behavior, where the exponent for the quantum transport is twice the exponent of its classical counterpart. For small-world networks, however, the measure shows rather a stretched exponential law but still the quantum transport outperforms the classical one. Some finite tree graphs have a few highly degenerate eigenvalues, such that, on the other hand, on them the classical transport may be more efficient than the quantum one.
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Affiliation(s)
- Oliver Mülken
- Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg i.Br., Germany.
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Mülken O, Bierbaum V, Blumen A. Coherent exciton transport in dendrimers and continuous-time quantum walks. J Chem Phys 2006; 124:124905. [PMID: 16599723 DOI: 10.1063/1.2179427] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We model coherent exciton transport in dendrimers by continuous-time quantum walks. For dendrimers up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site, we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes shows characteristic patterns and allows us to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or to be again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian.
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Affiliation(s)
- Oliver Mülken
- Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany.
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