High fidelity and robustness in population inversion is very desirable for many quantum control applications. We expand composite pulse schemes developed for two-level dynamics and present an analytic solution for the coherent evolution of an N-level quantum system with SU(2) symmetry, for achieving high fidelity and robust population inversion. Our approach offers a platform for accurate steering of the population transfer in physical multi-level systems, which is crucial for fidelity in quantum computation and achieving fundamental excitations in nuclear magnetic resonances and atomic physics. We also introduce and discuss the geometrical trajectories of these dynamics on the Majorana sphere as an interpretation, allowing us to gain physical insight on the dynamics of many-body or high-dimensional quantum systems.
Under the action of coherent periodic driving a generic quantum system will undergo Floquet heating and continuously absorb energy until it reaches a featureless thermal state. The phase-space constraints induced by certain symmetries can, however, prevent this and allow the system to dynamically form robust steady states with off-diagonal long-range order. In this work, we take the Hubbard model on an arbitrary lattice with arbitrary filling and, by simultaneously diagonalizing the two possible SU(2) symmetries of the system, we analytically construct the correlated steady states for different symmetry classes of driving. This construction allows us to make verifiable, quantitative predictions about the long-range particle-hole and spin-exchange correlations that these states can possess. In the case when both SU(2) symmetries are preserved in the thermodynamic limit we show how the driving can be used to form a unique condensate which simultaneously hosts particle-hole and spin-wave order.
We investigate the role of the global driving phase
Φ in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with closed-loop couplings, where external driving fields induce interference effects that strongly influence population transfer and symmetry properties of time-evolution. While full time-reversal symmetry requires
Φ=0,π, leading to a real Hamiltonian, we focus on a less restrictive transformation, the phase inversion (or complex conjugation of the Hamiltonian), under which population dynamics can remain symmetric even though coherences generally do not. We show that the presence of a dark (spectator) state is a sufficient condition for this population phase symmetry (P
ΦS), as it constrains the dynamics to reduced subspaces characterized by SU(2) or open-loop SU(3) evolution. We analyze this mechanism in three- and four-level systems and derive general conditions for P
ΦS that extend to generic
n-level configurations, with
n even. These findings provide practical guidelines for achieving robust control in quantum systems, with potential applications in quantum information processing and quantum computing.