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Bulletin of the American Physical Society

Quantum walk and localization dynamics of rotational excitations in disordered ensembles of polar molecules

Tianrui Xu, Roman V. Krems

Published Jan 21, 2015• 0 citations
OpenAlex

Abstract

We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale $t \sim 1$ sec. For 3D lattices with $55$ sites in each dimension and vacancy concentration $ 90~\%$, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2. Our results raise a general question whether quantum particles with long-range tunnelling can undergo quantum localization in 3D lattices with substitutional disorder.

Related papers

Quantum walk and Anderson localization of rotational excitations in disordered ensembles of polar molecules

T Xu, Roman V. Krems

We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t ∼ 1 s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.

arXiv:1501.05063•New Journal of Physics•Jun 17, 2015•10 citations

Localization of quantum particles with long-range hopping in 3D lattices of finite size

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Non-interacting particles with long-range hopping are known to be delocalized in disordered systems of infinite size. It is thus natural to assume that such particles can traverse any finite-size lattice. Here, we demonstrate that this is not generally true. The delocalization mechanism is induced by resonances between distant lattice sites. The number of such resonances diverges with the system size. For a finite-size lattice the number of resonances is finite and may not be sufficient to result in delocalization. We consider particles with long-range (dipolar) hopping in three-dimensional lattices with diagonal disorder and random dilution. We compute the wavepacket dynamics of particles placed in an individual lattice site, the inverse participation ratios and the fluctuations of the wavefunctions with disorder. We show that, for certain finite-size disordered lattices, particles remain localized within a finite volume much smaller than the lattice size, and that the wavefunctions exhibit the log-normal fluctuations characteristic of Anderson localization. We characterize the localization properties as functions of dilution and diagonal disorder. We combine our results with scaling theory to obtain the size dependence of the localization--diffusion crossover. Our results indicate that particles with long-range hopping undergo exponential localization in lattices of finite size, even macroscopically finite. Our phase diagrams illustrate a rather unusual phenomenon: quantum particles can diffuse through a lattice of size $10A$, but not through a lattice of size $A$.

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Numerical studies on correlations in dynamics and localization of two interacting particles in lattices

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Two interacting particles in lattices, in the absence of dissipation, can not distin- guish between attractive or repulsive interaction when the range of their tunnelling is limited to nearest neighbor sites. However, we find that, in the case of long-range tunnelling, the particles exhibit different dynamics for different types of interactions of the same strength. The nature of dynamical correlations between particles also becomes significantly different. For weak interactions, particles develop a character in correlation which is in between that of antiwalking and cowalking when the tunnelling is long-range. For strong interactions, particles cowalk independently of their statistics. A few recent experiments have demonstrated such effects of interactions on quantum walk of photons, atoms and spin excitations on various lattice platforms. In disordered lattices the effect of coherent backscattering makes particles localize to their initial position. We find that a weak repulsive interaction reduces localization and a strong interaction enhances localization. We also calculate the correlations between the particles in the disordered 1D and 2D systems. The effect of long-range tunnelling on localization of particles in disordered 1D systems has been explored. For large ordered or disordered lattices, computation of localization parameters becomes difficult. In these cases, an efficient recursive algorithm is used to calculate Green’s functions exactly. We extend such algorithm to disordered systems in both one and two dimensions. We also illustrate that this recursive algorithm maps directly to some graph structures like binary trees. We perform calculations for quantum walk of interacting particles on such graphs. The method is also used to calculate the properties of interacting particles on lattices with gauge fields. For disordered 2D lattices, we introduce and test approximations which produce accurate results and make the calculations more efficient. We examine the localization parameters for a broad range of interaction and disorder strengths and try to find differences among parameters within the range.

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Anderson Localization in Low-Dimensional Optical Lattices

Jan Major

Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the main fraction of atoms with the second immobilized fraction distributed randomly over the lattice. In low-dimensional systems there is no transition from the Anderson localized to the conducting phase, although in the presence of correlations a discrete set of extended states can exist. The first part of the thesis is devoted to properties of such states. In the finite size lattices, the presence of those states results in the appearance of `windows of transport' -- energy ranges, in which the localization length is longer than the system size.The analytical method of determining the extended states energies for correlations of generalized $N$-mers type is presented, along with a proof that indeed those states are extended in the infinite system. Subsequently, the way of experimental creation of this type of correlations is proposed, as well as the technique of generation of the disorder in the tunneling amplitudes, which significantly enhances tunability of the proposed energy filters. The second part of the thesis describes the method which allows to simulate a specific type of the disorder: random magnetic field. Systems of such a class, created in a two dimensional lattice using simultaneous fast periodic modulation of the lattice height and interactions with immobilized species, may allow in future to investigate the range of topics from the condensed matter physics, for example fractional quantum Hall effect at half-filling. In the thesis, the most interesting features observed upon investigation of such systems are presented. Especially, the anomalously low localization length for correlated disorder is explained.

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Transport and disorder-induced localization of ultracold Fermi gases

William McGehee

We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.

•Jul 14, 2015•0 citations

ROTATIONAL EXCITATIONS OF POLAR MOLECULES ON AN OPTICAL LATTICE: FROM NOVEL EXCITON PHYSICS TO QUANTUM SIMULATION OF NEW LATTICE MODELS

Marina Litinskaya, Roman V. Krems

Ultracold polar molecules trapped on an optical lattice is a many-body system that, under appropriate conditions, may support collective excitations reminiscent of excitons in solid state crystals. Here, we discuss the rotational excitations of molecules on an optical lattice leading to rotational Frenkel excitons. Apart from solid hydrogen, there is no other natural system that exhibits rotational excitons. The rotational excitons have unique properties that can be exploited for tuning non-linear exciton interactions and exciton-impurity scattering by applying an external electric field. We show that this can be used to explore the competing role of the dynamical and kinematic exciton-exciton interactions in excitonic energy transfer and to study quantum localization in a dynamically tunable disordered potential. The rotational excitons can also be used as a basis for quantum simulation of condensed matter models that cannot be realized with ultracold atoms. As an example, we discuss the possibility of engineering the Holstein model with polar molecules on an optical lattice.

arXiv:1208.0363•Annual review of cold atoms and molecules•Jan 27, 2013•2 citations
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t∼1t \sim 1t∼1 sec. For 3D lattices with 555555 sites in each dimension and vacancy concentration 90 % 90~\%90 %, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2. Our results raise a general question whether quantum particles with long-range tunnelling can undergo quantum localization in 3D lattices with substitutional disorder.
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t ∼ 1 s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.
Non-interacting particles with long-range hopping are known to be delocalized in disordered systems of infinite size. It is thus natural to assume that such particles can traverse any finite-size lattice. Here, we demonstrate that this is not generally true. The delocalization mechanism is induced by resonances between distant lattice sites. The number of such resonances diverges with the system size. For a finite-size lattice the number of resonances is finite and may not be sufficient to result in delocalization. We consider particles with long-range (dipolar) hopping in three-dimensional lattices with diagonal disorder and random dilution. We compute the wavepacket dynamics of particles placed in an individual lattice site, the inverse participation ratios and the fluctuations of the wavefunctions with disorder. We show that, for certain finite-size disordered lattices, particles remain localized within a finite volume much smaller than the lattice size, and that the wavefunctions exhibit the log-normal fluctuations characteristic of Anderson localization. We characterize the localization properties as functions of dilution and diagonal disorder. We combine our results with scaling theory to obtain the size dependence of the localization--diffusion crossover. Our results indicate that particles with long-range hopping undergo exponential localization in lattices of finite size, even macroscopically finite. Our phase diagrams illustrate a rather unusual phenomenon: quantum particles can diffuse through a lattice of size 10A10A10A, but not through a lattice of size AAA.
Two interacting particles in lattices, in the absence of dissipation, can not distin- guish between attractive or repulsive interaction when the range of their tunnelling is limited to nearest neighbor sites. However, we find that, in the case of long-range tunnelling, the particles exhibit different dynamics for different types of interactions of the same strength. The nature of dynamical correlations between particles also becomes significantly different. For weak interactions, particles develop a character in correlation which is in between that of antiwalking and cowalking when the tunnelling is long-range. For strong interactions, particles cowalk independently of their statistics. A few recent experiments have demonstrated such effects of interactions on quantum walk of photons, atoms and spin excitations on various lattice platforms. In disordered lattices the effect of coherent backscattering makes particles localize to their initial position. We find that a weak repulsive interaction reduces localization and a strong interaction enhances localization. We also calculate the correlations between the particles in the disordered 1D and 2D systems. The effect of long-range tunnelling on localization of particles in disordered 1D systems has been explored. For large ordered or disordered lattices, computation of localization parameters becomes difficult. In these cases, an efficient recursive algorithm is used to calculate Green’s functions exactly. We extend such algorithm to disordered systems in both one and two dimensions. We also illustrate that this recursive algorithm maps directly to some graph structures like binary trees. We perform calculations for quantum walk of interacting particles on such graphs. The method is also used to calculate the properties of interacting particles on lattices with gauge fields. For disordered 2D lattices, we introduce and test approximations which produce accurate results and make the calculations more efficient. We examine the localization parameters for a broad range of interaction and disorder strengths and try to find differences among parameters within the range.
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the main fraction of atoms with the second immobilized fraction distributed randomly over the lattice. In low-dimensional systems there is no transition from the Anderson localized to the conducting phase, although in the presence of correlations a discrete set of extended states can exist. The first part of the thesis is devoted to properties of such states. In the finite size lattices, the presence of those states results in the appearance of `windows of transport' -- energy ranges, in which the localization length is longer than the system size.The analytical method of determining the extended states energies for correlations of generalized NNN-mers type is presented, along with a proof that indeed those states are extended in the infinite system. Subsequently, the way of experimental creation of this type of correlations is proposed, as well as the technique of generation of the disorder in the tunneling amplitudes, which significantly enhances tunability of the proposed energy filters. The second part of the thesis describes the method which allows to simulate a specific type of the disorder: random magnetic field. Systems of such a class, created in a two dimensional lattice using simultaneous fast periodic modulation of the lattice height and interactions with immobilized species, may allow in future to investigate the range of topics from the condensed matter physics, for example fractional quantum Hall effect at half-filling. In the thesis, the most interesting features observed upon investigation of such systems are presented. Especially, the anomalously low localization length for correlated disorder is explained.
We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.
Ultracold polar molecules trapped on an optical lattice is a many-body system that, under appropriate conditions, may support collective excitations reminiscent of excitons in solid state crystals. Here, we discuss the rotational excitations of molecules on an optical lattice leading to rotational Frenkel excitons. Apart from solid hydrogen, there is no other natural system that exhibits rotational excitons. The rotational excitons have unique properties that can be exploited for tuning non-linear exciton interactions and exciton-impurity scattering by applying an external electric field. We show that this can be used to explore the competing role of the dynamical and kinematic exciton-exciton interactions in excitonic energy transfer and to study quantum localization in a dynamically tunable disordered potential. The rotational excitons can also be used as a basis for quantum simulation of condensed matter models that cannot be realized with ultracold atoms. As an example, we discuss the possibility of engineering the Holstein model with polar molecules on an optical lattice.