**SFB 925**Light induced dynamics and control of correlated quantum systems

# Project C9

### 2016

#### Theory of enhanced interlayer tunneling in optically driven high Tc superconductors

*J. Okamoto, A. Cavalleri, L. Mathey*

Motivated by recent pump-probe experiments indicating enhanced coherent c-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue-detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, non-equilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

#### Designing exotic many-body states of atomic spin and motion in photonic crystals

*M. T. Manzoni, L. Mathey, D. E. Chang*

Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. Here we investigate the strong coupling between atomic internal ("spin") degrees of freedom and motion, which arises from spin-dependent forces associated with the exchange of guided photons. We show that this system can realize a remarkable and extreme limit of quantum spin-orbital systems, where both the direct spin exchange between neighboring sites and the kinetic energy of the orbital motion vanish. We find that this previously unexplored system has a rich phase diagram of emergent orders, including spatially dimerized spin-entangled pairs, a fluid of composite particles comprised of joint spin-phonon excitations, phonon-induced Neel ordering, and a fractional magnetization plateau associated with trimer formation.

#### Magnus expansion approach to parametric oscillator systems in a thermal bath

*B. Zhu, T. Rexin, L. Mathey*

We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilization at second order, we find that the higher orders further renormalize the oscillator frequency, and additionally create a weakly renormalized effective temperature. The renormalized oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break-down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.

arXiv:1604.01010

http://arxiv.org/abs/1604.01010

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#### Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

*Marlon Nuske, L. Mathey, Eite Tiesinga*

We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultracold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency ∣∣Uf|/2π in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter Δ. The oscillation frequency of Δ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e., density-density) correlation functions oscillate at frequency ∣∣Uf|/2π as well as at its second harmonic. For a very deep lattice, with zero tunneling energy, the oscillations of momentum occupation numbers are undamped. Nonzero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. The damping occurs even for a finite-temperature initial BCS state, but not for a noninteracting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anticorrelations near the Dirac point.

### 2014

#### Noise correlations of two-dimensional Bose gases

*V. P. Singh, L. Mathey*

We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.

### 2013

#### Quantum Phases of quadrupolar Fermi gases in optical lattices

*S. G. Bhongale, L. Mathey, E. Zhao, S. F. Yelin, M. Lemeshko*

We introduce a new platform for quantum simulation of many-body systems based on non-spherical particles with zero dipole moment but possessing a significant value of the electric quadrupole moment. Considering a quadrupolar quantum gas trapped in a 2D optical lattice, we show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interactions results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and paves the way to create topological superfluid ground states of px + i py symmetry. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

Phys. Rev. Lett. 110, 155301 (2013)

http://arxiv.org/abs/1211.3317

### 2012

#### Unconventional Spin Density Waves in Dipolar Fermi Gases

*S. G. Bhongale, L. Mathey, S. Tsai, C. W. Clark, E. Zhao*

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.

Phys. Rev. A 87, 043604 (2012)

http://arxiv.org/abs/1209.2671

#### Decay of a superfluid current of ultra-cold atoms in a toroidal trap

*Amy C. Mathey, Charles W. Clark, L. Mathey*

Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into rotation via a Gauss-Laguerre beam. A potential barrier is then placed in the trap to study the decay of the superflow. We find that the current decays via thermally activated phase slips, which can also be visualized as vortices crossing the barrier region in radial direction. Adopting the notion of critical velocity used in the experiment, we determine it to be lower than the local speed of sound at the barrier. This result is in agreement with the experimental findings, but in contradiction to the predictions of the Gross-Pitaevskii equation. This emphasizes the importance of thermal fluctuations in the experiment.