Recent Publications

Recent publications

Researcher ID C-6654-2009

Many studies of Floquet engineering focus on either periodically driving an external potential, or driving the interaction term (see here for one example). One possibility is left: to periodically drive the tunnelling, or kinetic energy. In our paper, published in the New Journal of Physics, we investigate the effects of this kind of "kinetic driving" in the Bose-Hubbard model. By using Floquet analysis, we derive the static effective Hamiltonian that arises in the limit of high driving frequency which has the novel feature that nearest-neighbor single-particle hopping processes are suppressed, but all even higher-order processes are allowed, and can be arbitrarily long-ranged. Unusual many-body features arise from the combined effect of the nonlocal interactions and correlated tunneling.

In particular, at a critical value of the driving, the system passes from a Mott insulator to a superfluid formed by two quasi-condensates with opposite nonzero momenta. This fragmented superfluid consists of a coherent superposition of the two condensates, forming a Schrodinger cat-like state, whose properties can be described well as a Luttinger liquid. We extract the spectrum of the system's collective excitations, and locate the critical driving strength by evaluating the Luttinger liquid parameter. We further verify that this point coincides with the vanishing of the superconducting gap and the macroscopic occupation of the two condensates.

Together with Germán Sierra (UAM-CSIC) we have shown how we can solve the "inverse problem" of designing a periodic driving potential to give a certain behaviour of the quasi energy spectrum. This is much more difficult than the standard problem in which you calculate the quasienergies from a given driving potential.

We have applied this technique to the problem of finding the zeros of the Riemann zeta function. With the driving potential we use the quasierergies become degenerate at the Riemann zeros. This has a physical consequence for a cold atom gas, in that its rate of expansion becomes frozen. This means that the Riemann zeros can be measured directly in experiment, using a driven gas of ultracold atoms essentially as an analogue computer, and perhaps indicates an alternative way to approach the Polya-Hilbert conjecture by introducing time-dependent driving.

We have previously shown how to create hopping phases for cold atoms held in a one-dimensional lattice, using a periodic driving potential (or "shaking the lattice"). This allows us to control the expansion and centre-of-mass motion of a condensate. However, to create a synthetic gauge field in a 2D lattice - the logical next step - is not as simple as might appear. A pioneering proposal by Kolovsky was shown by us to contain a flaw. We have found a way to escape this problem by developing a new scheme which we call "split-driving" in analogy with the well-known "split-operator" technique used in quantum simulation. Basically the lattice is driven under two separate Hamiltonians. Initially it is shaken in the x-direction while tunneling in the y-direction is suppressed. Then tunneling is suppressed in the x-direction while the y-tunneling is restored, and the process repeated. A full description is given in our paper.

A figure from this paper, showing how the quasienergies of the system mimic the Hofstadter butterfly structure, was selected for the Phys. Rev. A "Kaleidoscope" feature:

In collaboration with Cristiane de Morais Smith and Marco Di Liberto, based at the University of Utrecht, we have investigated the effect of periodically varying the interaction strength of a Bose-Einstein condensate (for example, by oscillating a magnetic field about a Feshbach resonance). The result is an unusual hopping Hamiltonian, in which the amplitude of the hopping depends on the filling of the initial and final state - a so-called "correlated hopping" model. Such models have some unusual properties, such as eta-superconductivity, and this provides one of the first means to physically produce such a system.

In previous work we in the Madrid group have shown a particular way in which a periodically-driven BEC can display a ratchet effect, when the relevant space and time symmetries of the system are broken. The origin of this effect is rather profound, and we have discovered that it can be understood as arising from a novel form of Josephson effect, which we term the "orbital Josephson effect". My student, Martin Heimsoth, has prepared a short introduction to this phenomenon.

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