Dissipative Floquet engineering of gapped many-body phases using thermal baths

Abstract

Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of the system so that it becomes described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, already the preparation of such states is challenged by excitations due to imperfect adiabatic dynamics, especially when a phase transition has to be passed. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap. Our approach relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state, but generally non-thermal occupations of excited states of the effective Hamiltonian. We use the Floquet-Born-Markov master equation to verify the proposed strategy for the example of a strongly driven Bose-Hubbard chain with an effective gapped Mott-insulator ground state.

Figures (4)

• Figure 1: Sketch of a many-body quasienergy spectrum at high frequencies, using the example of the driven Bose-Hubbard model, with scaled interaction strength $U/J$. In a first approximation it is given by the overlapping spectra of $\hat{H}_\text{eff}+m\hbar\Omega$ (shown with different colors for different $m$). For large $U/J$ it consists of bands above a gapped ground state, corresponding to different numbers and configurations of particle-hole excitations (as those sketched on the right) dispersed by tunneling. Resonant coupling leads to tiny avoided crossings between states of different $m$ (inset). The dominant bath-induced transitions into and out of the $m=0$ copy of the $\hat{H}_\text{eff}$ ground state are labeled $(a)$ and $(b)$, respectively.
• Figure 2: Steady-state ground-state probability $P_0=\langle v_0|\hat{\rho}|v_0\rangle$ for 4 particles on 4 sites, with $\hbar\Omega=25J$, $\beta^{-1}=0.3J$, $E_{\mathrm{cut}} = \mathrm{max}(U,J)$, calculated using (a) the Pauli equation (\ref{['eq:PauliEquation']}), (c,d) the Redfield equation (\ref{['eq:Redfield']}) at a coupling strength $\gamma_{(c)}=0.0001$, $\gamma_{(d)}=0.04$. The red and green lines mark the parameter regime shown in Fig. \ref{['fig:UScan1/3ResonanzL=4']} for other intermediate $\gamma$. The black line indicates the superfluid to Mott-insulator transition. (b) shows the ground state population in the Mott regime obtained by the two-rate model. The white areas in (d) mark regions where the Redfield equation gives non-positive density operators.
• Figure 3: Colored lines: Same as Fig. \ref{['fig:DoubleMapL=4']}(c,d), but at fixed driving strength $\alpha=0.5$ and different couplings $\gamma$. Black line: Part of the quasienergy spectrum close to the ground state energy of the effective Hamiltonian (right axis). At the avoided crossings, the weakly coupled system shows dips in the ground state occupation, indicating Floquet heating. For stronger dissipation these dips are reduced and also displaced by the Lamb shift (the latter is exemplified by the colored shading of the same resonance at different $\gamma$).
• Figure 4: Same as Fig. \ref{['fig:UScan1/3ResonanzL=4']}, but $P_0$ is only shown for $\gamma=10^{-4}$ (red line) and the full quasienergy spectrum is plotted (black lines).