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arXiv:2202.02743 · Physical Review A

Simultaneous cooling by measuring one ancillary system

Jia‐shun Yan, Jun Jing

Published May 27, 2022• 9 citations
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Abstract

We present a simultaneous-cooling protocol for a double-resonator system via projective measurements on an ancillary $V$-type qutrit. Through repeated measurements on the ground state of the ancillary system, the two resonators can be cooled down to their respective ground states from thermal states. With respect to the measurement-based cooling, an optimized measurement interval ${\ensuremath{\tau}}_{\mathrm{opt}}$ is analytically obtained, which is inversely proportional to the collective thermal Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{th}}$ as a function of the resonators' average population of the last round. Under about only 20 optimized measurements, the average population of the target resonators can be reduced by six orders in magnitude. Our simultaneous or collective cooling protocol is scalable to the systems with more numbers of resonators and robust to the fluctuation in the resonator frequency. Also we discuss the robustness of our cooling protocol against the thermal environment and the measurement error.

DOI
10.1103/physreva.105.052607

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We present a simultaneous-cooling protocol for a double-resonator system via projective measurements on an ancillary VVV-type qutrit. Through repeated measurements on the ground state of the ancillary system, the two resonators can be cooled down to their respective ground states from thermal states. With respect to the measurement-based cooling, an optimized measurement interval \ensuremathτopt{\ensuremath{\tau}}_{\mathrm{opt}}\ensuremathτopt​ is analytically obtained, which is inversely proportional to the collective thermal Rabi frequency \ensuremathΩth{\mathrm{\ensuremath{\Omega}}}_{\mathrm{th}}\ensuremathΩth​ as a function of the resonators' average population of the last round. Under about only 20 optimized measurements, the average population of the target resonators can be reduced by six orders in magnitude. Our simultaneous or collective cooling protocol is scalable to the systems with more numbers of resonators and robust to the fluctuation in the resonator frequency. Also we discuss the robustness of our cooling protocol against the thermal environment and the measurement error.
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A quantum resonator in a thermal-equilibrium state with a high temperature has a large average population and is featured with significant occupation over Fock states with a high excitation number. The resonator could be cooled down via continuous measurements on the ground state of a coupled two-level system (qubit). We find, however, that the measurement-induced cooling might become inefficient in the high-temperature regime. Beyond the conventional strategy, we introduce strong driving between the excited state of the qubit and an external level. It can remarkably broaden the cooling range in regard to the nonvanishing populated Fock states of the resonator. Without any precooling procedure, our strategy allows a significant reduction of the populations over Fock states with a high excitation number, giving rise to nondeterministic ground-state cooling after a sequence of measurements. The driving-induced fast transition constrains the resonator and the ancillary qubit at their ground state upon measurement and then simulates the quantum Zeno effect. Our protocol is applied to cool down a high-temperature magnetic resonator. Additionally, it is generalized to a hybrid cooling protocol by interpolating the methods with and without strong driving, which can accelerate the cooling process and increase the overlap between the final state of the resonator and its ground state.
A quantum resonator in a thermal-equilibrium state with a high temperature has a large average exciton number and has a significant occupation over the high Fock-states. The resonator could be cooled down through constant measurements on the ground state of a coupled two-level system (qubit). We find, however, that the measurement-induced cooling might become inefficient in the high-temperature regime. Beyond the conventional strategy, we propose a measurement-induced-cooling protocol via acting a strong interaction outside the space of the resonator-qubit system. In particular, the excited state of the two-level system is coupled to an outside state through a driving field. The strong interaction between these two states can greatly enlarge the cooling range in regard to the non-vanishing populated Fock-states of the resonator. Without any pre-cooling procedure, acting outside allows a significant reduction on the populations over the high Fock-states and then the ground-state cooling after a sequence of measurements. The fast transition induced by a strong acting-outside constrains the ancillary system at its ground state and then simulates a quantum Zeno effect, that consistently provides a possible realization for measurements required for cooling. Our protocol is applied to cool down a high-temperature magnetic resonator. It is then generalized to a hybrid cooling protocol by interpolating the methods with and without acting on the outside, which can accelerate the cooling process and promote the overlap between the final state of the resonator and its ground state.
Abstract Nondeterministic measurement‐based techniques are efficient in reshaping the population distribution of a quantum system but suffer from a limited success probability of holding the system in the target state. To save the experimental cost, a two‐step protocol is proposed to cool a resonator down to the ground state with a near‐unit probability by exploiting the state‐engineering mechanisms of both conditional and unconditional measurements on an ancillary qubit. In the first step, the unconditional measurements on the ancillary qubit are applied to reshape the target resonator from a thermal state to a reserved Fock state. The measurement sequence can be efficiently optimized by reinforcement learning for maximum fidelity. In the second step, the population on the reserved state can be faithfully transferred in a stepwise way to the resonator's ground state with a near‐unit fidelity by the conditional measurements on the qubit. Properly designing the projection operator and the measurement interval enables the Kraus operator to act as a lowering operator for neighboring Fock states. Through dozens of measurements in all, the initial thermal average population of the resonator can be reduced by five orders in magnitude with a success probability of over 95%.
We propose an approach for cooling both an artificial atom (e.g., a flux qubit) and its neighboring quantum system, the latter modeled by either a quantum two-level system or a quantum resonator. The flux qubit is cooled by manipulating its states, following an inverse process of state population inversion, and then the qubit is switched on to resonantly interact with the neighboring quantum system. By repeating these steps, the two subsystems can be simultaneously cooled. Our results show that this cooling is robust and effective, irrespective of the chosen quantum systems connected to the qubit.
We solve the closed-system problem of cooling MMM qubits, selected from NNN identical thermal qubits, to the lowest common local temperature allowed by unitarity. The optimal protocol consists of two conceptually distinct steps. First, a passive rearrangement assigns the largest eigenvalues of the initial state to target sectors of lowest Hamming weight, thereby minimizing the total target energy. Second, a target-only complex-Hadamard transformation within each fixed-Hamming-weight subspace equalizes the one-qubit target marginals without changing any target-sector probability or the total energy. Consequently, imposing a common local temperature costs neither cooling depth nor additional work: the constrained optimum coincides with the unconstrained passive minimum for every N>MN>MN>M and every initial temperature. The complex-Hadamard correction may nevertheless be costly at the circuit level. We therefore derive an exact arithmetic criterion for when the same optimum can be attained by a temperature-independent computational-basis permutation alone, and exhaustively classify the resulting finite-size islands of feasibility for M+2≤N≤128M+2\leq N\leq 128M+2≤N≤128. At isolated temperatures, further optimal permutations can arise through numerical cancellations between different thermal eigenvalue shells. These alternative realizations may reduce implementation complexity, but they cannot improve the cooling curve already attained by the universal protocol. We also derive the exact cooling curve, prove that at least two ancillary qubits are necessary and sufficient for nontrivial cooling, and show that joint many-target cooling can strictly outperform parallel single-target strategies.