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arXiv:0904.2614 · Physical Review A

Control of bound-pair transport by periodic driving

Kazue Kudo, T. Boness, T. S. Monteiro

Published Dec 4, 2009• 34 citations
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Abstract

We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (such as the ferromagnetic $XXZ$ model) as well as ultracold fermionic atoms described by the attractive Hubbard model. We show that a well-known phenomenon seen in periodically driven systems---the renormalization of the exchange coupling strength---acts selectively on bound pairs of spins (atoms), relative to magnon (bare atom) states. Thus one can control the direction and speed of transport of bound pair relative to magnon (unpaired) atom states, and thus coherently achieve spatial separation of these components. Applications to recent experiments on transport with fermionic atoms in optical lattices which consist of mixtures of bound pairs and bare atoms are discussed.

DOI
10.1103/physreva.80.063409

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We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (such as the ferromagnetic XXZXXZXXZ model) as well as ultracold fermionic atoms described by the attractive Hubbard model. We show that a well-known phenomenon seen in periodically driven systems---the renormalization of the exchange coupling strength---acts selectively on bound pairs of spins (atoms), relative to magnon (bare atom) states. Thus one can control the direction and speed of transport of bound pair relative to magnon (unpaired) atom states, and thus coherently achieve spatial separation of these components. Applications to recent experiments on transport with fermionic atoms in optical lattices which consist of mixtures of bound pairs and bare atoms are discussed.
We propose a new method to control the directed quantum transport of ultracold atoms in a one-dimensional optical lattice. In this proposal, the effective tunneling between the neighboring sites can be adjusted via coherent destruction of tunneling by tuning the phase of the external field, instead of using the driving field intensity or the frequency, thus the directed quantum transport of ultracold atoms can be coherently controlled in a much easier manner. Our proposal overcomes the major drawback of the method used by Creffield et al. [ Phys. Rev. Lett. 99 (2007) 110501 ], and can be implemented, in principle, in any one-dimensional optical lattice. Some potential applications of the scheme are also discussed.
We propose using ultracold fermionic atoms trapped in a periodically shaken optical lattice as a quantum simulator of the $t\text{\ensuremath{-}}J$ Hamiltonian, which describes the dynamics in doped antiferromagnets and is thought to be relevant to the problem of high-temperature superconductivity in the cuprates. We show analytically that the effective Hamiltonian describing this system for off-resonant driving is the $t\text{\ensuremath{-}}J$ model with additional pair hopping terms, whose parameters can all be controlled by the drive. We then demonstrate numerically using tensor network methods for a one-dimensional (1D) lattice that a slow modification of the driving strength allows near-adiabatic transfer of the system from the ground state of the underlying Hubbard model to the ground state of the effective $t\text{\ensuremath{-}}J$ Hamiltonian. Finally, we report exact diagonalization calculations illustrating the control achievable on the dynamics of spin-singlet pairs in 2D lattices utilizing this technique with current cold-atom quantum-simulation technology. These results open new routes to explore the interplay between density and spin in strongly correlated fermionic systems through their out-of-equilibrium dynamics.
Controlling and stabilising collective phases of many-body quantum systems is a problem of deep fundamental and technological interest. In this thesis, we perform a theoretical investigation on how useful quantum phases may be engineered in strongly correlated fermionic lattice systems, especially through periodic driving. We first compute the phase diagram of the one-dimensional t–J model with the addition of non-standard pair hopping terms. We show that at dilute fillings these terms enhance superconductivity while, counter- intuitively, suppressing it at large fillings. We argue that this is due to dynamical constraints originating from the fact that local pairs cannot overlap. We conjecture that these constraints may play a more significant role in the physics of two-dimensional systems where the t–J model is studied as a candidate model of high-Tc superconductivity. We begin to investigate these dynamical constraints on a ladder geometry. We then study the fermionic Hubbard model under periodic driving. We show that the driving induces a strong and robust singlet-pairing effect consistent with a superconducting state. This could provide a new mechanism for light-induced superconductivity in some classes of strongly cor- related materials. We show using Floquet theory that the dynamics of the driven Hubbard model are described precisely by the t–J model studied in the previous section. As the driven Hubbard model is also implementable with ultracold fermions in an optical lattice, our results could lead to their use as a quantum simulator for a broad class of candidate models for high-Tc superconductivity.
We study the one-dimensional attractive fermionic Hubbard model under the influence of periodic driving with the time-dependent density matrix renormalization group method. We show that the system can be driven into an unconventional pairing state characterized by a condensate made of Cooper pairs with a finite center-of-mass momentum similar to a Fulde-Ferrell state. We obtain results both in the laboratory and the rotating reference frames demonstrating that the momentum of the condensate can be finely tuned by changing the ratio between the amplitude and the frequency of the driving. In particular, by quenching this ratio to the value corresponding to suppression of the tunneling and the Coulomb interaction strength to zero, we are able to ``freeze'' the condensate. We finally study the effects of different initial conditions and compare our numerical results to those obtained from a time-independent Floquet theory in the large frequency regime. Our work offers the possibility of engineering and controlling unconventional pairing states in fermionic condensates.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.
Abstract Magnon excitations play an important role in understanding quantum magnetism and magnon bound states observed with ultracold atoms in optical lattices. Here, we investigate how gradient magnetic field and periodically modulated spin-exchange strength affect the two-magnon excitations. In the Stark resonance where the driving frequency matches and smooths the potential bias, the system gains translational invariance in both space and time in the rotating frame, and thus we can develop a Floquet–Bloch band theory for two magnons. We find a new kind of bound states with relative distance no less than two sites, apart from the conventional bound states with relative distance at one site, which indicates the modulation-induced long-range interaction. We analytically derive an effective Hamiltonian via the many-body perturbation theory for a deeper understanding of such novel bound states and explore the interplay between these two types of bound states. Moreover, we propose to probe modulation-induced bound states via quantum walks. Our study not only provides a scheme to form long-range magnon bound states, but also lays a cornerstone for engineering exotic quantum states in multi-particle Floquet systems.