Speeding up and slowing down the relaxation of a qubit by optimal control

Abstract

We consider a two-level quantum system prepared in an arbitrary initial state and relaxing to a steady state due to the action of a Markovian dissipative channel. We study how optimal control can be used for speeding up or slowing down the relaxation towards the fixed point of the dynamics. We analytically derive the optimal relaxation times for different quantum channels in the ideal ansatz of unconstrained quantum control (a magnetic field of infinite strength). We also analyze the situation in which the control Hamiltonian is bounded by a finite threshold. As byproducts of our analysis we find that: (i) if the qubit is initially in a thermal state hotter than the environmental bath, quantum control cannot speed up its natural cooling rate; (ii) if the qubit is initially in a thermal state colder than the bath, it can reach the fixed point of the dynamics in finite time if a strong control field is applied; (iii) in the presence of unconstrained quantum control it is possible to keep the evolved state indefinitely and arbitrarily close to special initial states which are far away from the fixed points of the dynamics.

11 pages, 6 figures

References in corpus (10)

• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Singular extremals for the time-optimal control of dissipative spin 1/2 particles
• Communication at the quantum speed limit along a spin chain
• Time-optimal control of a two-level dissipative quantum system
• Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
• Optimal coherent control to counteract dissipation
• Cooling through optimal control of quantum evolution
• Optimal Control for Open Quantum Systems: Qubits and Quantum Gates

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