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Measurement-based cooling of a nonlinear mechanical resonator

R Puebla, Obinna Abah, M Paternostro

Published Jun 15, 2020• 0 citations
Publisher

Abstract

We propose two measurement-based schemes to cool a nonlinear mechanical resonator down to energies close to that of its ground state. The protocols rely on projective measurements of a spin degree of freedom, which interacts with the resonator through a Jaynes-Cummings interaction. We show the performance of these cooling schemes, that can be either concatenated—i.e., built by repeating a sequence of dynamical evolutions followed by projective measurements—or single-shot. We characterize the performance of both cooling schemes with numerical simulations and pinpoint the effects of decoherence and noise mechanisms. Due to the ubiquity and experimental relevance of the Jaynes-Cummings model, we argue that our results can be applied in a variety of experimental setups.

DOI
10.25405/ncl.34452360

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We propose two measurement-based schemes to cool a nonlinear mechanical resonator down to energies close to that of its ground state. The protocols rely on projective measurements of a spin degree of freedom, which interacts with the resonator through a Jaynes-Cummings interaction. We show the performance of these cooling schemes, that can be either concatenated—i.e., built by repeating a sequence of dynamical evolutions followed by projective measurements—or single-shot. We characterize the performance of both cooling schemes with numerical simulations and pinpoint the effects of decoherence and noise mechanisms. Due to the ubiquity and experimental relevance of the Jaynes-Cummings model, we argue that our results can be applied in a variety of experimental setups.
We propose two measurement-based schemes to cool a nonlinear mechanical resonator down to energies close to that of its ground state. The protocols rely on projective measurements of a spin degree of freedom, which interacts with the resonator through a Jaynes-Cummings interaction. We show the performance of these cooling schemes, that can be either concatenated---i.e., built by repeating a sequence of dynamical evolutions followed by projective measurements---or single-shot. We characterize the performance of both cooling schemes with numerical simulations and pinpoint the effects of decoherence and noise mechanisms. Due to the ubiquity and experimental relevance of the Jaynes-Cummings model, we argue that our results can be applied in a variety of experimental setups.
We introduce a novel technique for efficiently cooling many-body quantum systems with unknown Hamiltonians down to their ground states with a high fidelity. This technique involves initially applying a strong external field followed by a sequence of single-degree-of-freedom (single-qubit) measurements and radio frequency pulses to polarize the system along the field direction. Subsequently, the field is adiabatically switched off, allowing the system to evolve toward its ground state as governed by the quantum adiabatic theorem. We present numerical simulation results demonstrating the effectiveness of the technique applied to quantum spin chains with long-range and short-range interactions as prototypes for many-body quantum systems.
Cooling a quantum system to its ground state is important for the characterization of non-trivial interacting systems, and in the context of a variety of quantum information platforms. In principle, this can be achieved by employing measurement-based passive steering protocols, where the steering steps are predetermined and are not based on measurement readouts. However, measurements, i.e., coupling the system to auxiliary quantum degrees of freedom, is rather costly, and protocols in which the number of measurements scales with system size will have limited practical applicability. Here, we identify conditions under which measurement-based cooling protocols can be taken to the dilute limit. For two examples of frustration-free one-dimensional spin chains, we show that steering on a single link is sufficient to cool these systems into their unique ground states. We corroborate our analytical arguments with finite-size numerical simulations and discuss further applications.
Nonlinear operations are essential for quantum information processing. We propose a way of implementing a class of nonlinear operations by sequential application of conditional gates based on Jaynes-Cummings (JC) interaction and projective measurements. The scheme has many advantages over the previously proposed all-optical methods and can be applied in several available experimental platforms, such as cavity quantum electrodynamics, trapped ions, and others. We demonstrate performance of the approach on the example of the cubic nonlinearity. We show several different ways in which the full nonlinear operation can be decomposed into sequences of the individual gates, and we compare their performance.
Fock states and their superpositions are exotic test beds for nonclassical physics and valuable resources for quantum technologies. We provide a simple protocol for the quantum measurement to generate an arbitrary Fock state and certain superposed Fock states from a coherent state of a target resonator, without any carefully tailored driving. This conditional protocol can be efficiently constructed by a sequence of joint free evolution of the resonator and an ancillary qubit, which are coupled via a Jaynes-Cummings interaction, and projective measurements on the qubit. By properly choosing the duration of each evolution-measurement cycle and the initial state of the resonator, we can generate a desired Fock state $|n\ensuremath{\rangle}$ and a superposed Fock state $(|0\ensuremath{\rangle}+|n\ensuremath{\rangle})/\sqrt{2}, n\ensuremath{\sim}10$, with a fidelity over 9999%99 in less than 30 measurements. Moreover, our protocol can be extended straightforwardly to the generation of a Bell-like state $(|00\ensuremath{\rangle}+|nn\ensuremath{\rangle})/\sqrt{2}$ with multiple excitations in a double-resonator system. We also calculate the outcome fidelity and the success probability of our protocol in the presence of decoherence.