Coherent Control of Dressed Matter Waves

Abstract

By moving the pivot of a pendulum rapidly up and down one can create a stable position with the pendulum's bob above the pivot rather than below it [1]. This surprising and counterintuitive phenomenon is a widespread feature of driven systems and carries over into the quantum world. Even when the static properties of a quantum system are known, its response to an explicitly timedependent variation of its parameters may be highly nontrivial, and qualitatively new states can appear that were absent in the original system. In quantum mechanics the archetype for this kind of behaviour is an atom in a radiation field, which exhibits a number of fundamental phenomena such as the modification of its g-factor in a radiofrequency field [2] and the dipole force acting on an atom moving in a spatially varying light field [3]. These effects can be successfully described in the so-called dressed atom picture [4]. Here we show that the concept of dressing can also be applied to macroscopic matter waves [5], and that the quantum states of "dressed matter waves" can be coherently controlled. In our experiments we use BoseEinstein condensates in driven optical lattices and demonstrate that the many-body state of this system can be adiabatically and reversibly changed between a superfluid and a Mott insulating state [6, 7, 8] by varying the amplitude of the driving. Our setup represents a versatile testing ground for driven quantum systems, and our results indicate the direction towards new quantum control schemes for matter waves.An atom in a radiation field can be described in the dressed atom picture [4] (or in equivalent approaches using, e.g., Floquet quasienergy states) in which the modified properties of the driven system arise from "dressing" the atom's electronic states with the photons of the radiation field. This concept can also be applied to macroscopic matter waves in driven periodic potentials [5], where the "dressing" is provided by the oscillatory motion of the lattice potential. In analogy to the dressed atom picture, such "dressed matter waves" can exhibit new properties absent in the original system and thus allow enhanced control of its quantum states. Here we demonstrate that matter waves can be adiabatically transferred into a well-defined Floquet quasienergy state of a driven periodic potential while preserving their quantum coherence.Cold atoms in optical lattices [7] can be described in the Bose-Hubbard model by the parameter U/J, where J is the hopping term relating to tunneling between adjacent sites, and U is the on-site interaction energy (see Fig. 1a). When U/J is small, tunneling dominates and the atoms are delocalized over the lattice, whereas a large value means that the inter- action term is large compared to J and phase coherence is lost through the formation of number-squeezed states with increased quantum phase fluctuations. At a critical value of U/J the system undergoes a quantum phase transition to a Mott insulator state. Using optical lattices one can tune U/J by changing the lattice dept...

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

“…Theoretical models based on Floquet's theorem are being developed to simulate systems in regimes otherwise inaccessible in conventional condensed matter materials [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . Experimentally, cold atoms' unique controllability was employed to observe dynamical localisation and phase-coherence in strongly shaken bosonic systems [19][20][21][22][23][24] . This paved the way towards generating extremely strong artificial magnetic fields 25 in lattice models, which recently culminated in the realisation of the Harper-Hofstadter model 26,27 , the Quantum Spin Hall Effect 28,29 , and Floquet topological insulators 30,31 .…”

Merging and alignment of Dirac points in a shaken honeycomb optical lattice

“…A periodic shaking of the optical lattice, up to the kHz frequency range, has been implemented by placing one of the mirrors used to create the optical lattice on a piezoelectric material, such that the mirror can be moved back and forth in the direction of the beam [13,14]. The Floquet formalism shows that the hopping energy of the atoms in the shaken lattice is renormalized by a Bessel function, as a function of the shaking frequency and amplitude, thus allowing both the magnitude and the sign of the hopping parameter to change.…”

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

“…Treating interactions in such a non-perturbative way is difficult in periodically-driven systems [5][6][7][8][9][10], which have received unprecedented attention following the realisation of dynamical localisation [11][12][13][14][15], artificial gauge fields [16][17][18][19][20][21][22], models with topological [23][24][25][26][27][28] and statedependent [29] bands, and spin-orbit coupling [30,31]. In this paper, we consider strongly-interacting periodicallydriven systems and show how the SWT can be extended to derive effective static Hamiltonians of non-equilibrium setups.…”

“…this, we choose a one-dimensional system with the driving protocol f jσ (t) = jA cos Ωt, which was realised experimentally by mechanical shaking [12,[12][13][14]. Unlike offresonant driving, resonance drastically alters the effective Hamiltonian by enabling the lowest-order term H (0) eff : on resonance, the doublon-holon (dh) creation/annihilation terms h † survive the time-averaging, and the leadingorder effective Hamiltonian reads…”