Spectrally controlled dissipation in a target subsystem

TL;DR

This work introduces a microscopic ancilla+target Hamiltonian that enables spectrally controlled dissipation on the target, allowing it to reach either a pure or a tunable mixed steady state depending on the bath spectrum and target energies. By formulating the dynamics as a chain-like process and applying spectral measure theory, the authors derive conditions under which the target equilibrates, contrasting this mechanism with conventional Lindblad dynamics that lack spectral gating. They demonstrate qubit-reset and mixed-state preparation via spectral control and extend the framework to multi-state targets, showing selective decay to preferred ground states. The results offer a design principle for engineered dissipation and autonomous quantum control, with potential applications in modeling bath dynamics and implementing robust qubit reset and error-mitigation schemes in quantum technologies.

Abstract

We present a microscopic Hamiltonian time-evolution on an ancilla+target system that evolves the target to a steady state. Using this description, we demonstrate the potential of a spectrally controllable dissipator: Depending on the energy scale of the target, the subsystem reaches the intended steady state or remains partially trapped in the initial state. For a steady state which is pure, this protocol can function as an autonomous qubit reset. We can also choose a mixed steady state so that this functions as a tunable mixed-state preparation. With a particular dissipative condition, we guarantee the equilibration to the steady-state with spectral measure theory. This type of spectral control over dissipation is not present in the common Lindblad description of open systems. Our construction establishes a new design principle for engineered dissipation and opens a pathway toward tunable autonomous quantum control.

Figures (3)

• Figure 1: Example of spontaneous decay from state $|1\rangle$ to state $|0\rangle$. The Lindblad description (a) is independent of the state energies $E_0$ and $E_1$, while the microscopic description (b) allows decay only under the spectral condition $\mu < 1$. (a) Lindblad description with $\Gamma = 1$. The occupation number decays the same for any energies $E_0$ of $|0\rangle$ and $E_1$ of $|1\rangle$. (b) Microscopic description with $B = 1$, $C = 1$, and $\mu = 0,\,0.7,\,1.4,\,2.1$. The decay occurs fully for $\mu=0$ and $\mu=0.7$. (c) Phase diagram from eq. \ref{['decay']} showing the decay region in middle green area.
• Figure 2: Controllable dissipation. This only implements the transition to the target state $|E_0\rangle$ for certain initial states. This is described in Example 4. Only the initial states $|0\rangle \otimes |E_0 \rangle$ and $|0\rangle \otimes |E_1 \rangle$ end in steady states with full occupation in $|E_0\rangle$. Therefore, this implements a reset of the $|E_1 \rangle$ state to $|E_0\rangle$ using the ancilla coupling.
• Figure 3: Plotting the occupation $\langle n_j \rangle=\langle e_j^\dag e_j \rangle$ as a function of time $t$ and position $j$. We time evolve with $\mu=0.5$, $B=1$, $C=0.5$. For a finite system with $L=80$ sites, the particle-wave reaches the boundary at $t\approx40=L/2B$.

Theorems & Definitions (2)

• Theorem 1
• Theorem 2