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Physical Review A

Single-step arbitrary control of mechanical quantum states in ultrastrong optomechanics

Luigi Garziano, Roberto Stassi, Vincenzo Macrí, Salvatore Savasta, Omar Di Stefano

Published Feb 5, 2015• 23 citations
Publisher

Abstract

We describe how ultrastrong interactions in optomechanical systems can be used to force the system ground state to evolve into an arbitrary quantum state of mechanical motion in a completely controlled and deterministic manner. If the target quantum state is a superposition of $N$ Fock states, it can be obtained by applying in single-step $N$ classical optical signals of different frequencies for a common time interval. This protocol can be applied to various strongly interacting quantum systems as trapped ions beyond the Lamb-Dicke regime and cavity QED into the ultrastrong coupling regime.

DOI
10.1103/physreva.91.023809

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We describe how ultrastrong interactions in optomechanical systems can be used to force the system ground state to evolve into an arbitrary quantum state of mechanical motion in a completely controlled and deterministic manner. If the target quantum state is a superposition of NNN Fock states, it can be obtained by applying in single-step NNN classical optical signals of different frequencies for a common time interval. This protocol can be applied to various strongly interacting quantum systems as trapped ions beyond the Lamb-Dicke regime and cavity QED into the ultrastrong coupling regime.
The observation of single-photon optomechanical effects is a desired task in cavity optomechanics. However, the realization of ultrastrong optomechanical interaction remains a big challenge. Here we present an all-optical scheme to simulate ultrastrong optomechanical coupling based on a Fredkin-type interaction, which consists of two exchange-coupled modes with the coupling strength depending on the photon number in another controller mode. This coupling enhancement is assisted by the displacement amplification according to the physical idea of the Bogoliubov approximation, which is realized by utilizing a strong driving to pump one of the two exchanging modes. Our numerical simulations demonstrate that the enhanced optomechanical coupling can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. We also show the creation of macroscopic quantum superposed states and the implementation of a weak-to-strong transition for quantum measurement in this system. This work will pave the way to quantum simulation of single-photon optomechanical effects with current experimental platforms.
We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest setup of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The PT phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.
Abstract Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of ‘single-photon strong coupling’, where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic motion to the much narrower cavity-dressed atomic resonance frequency. We discuss and optimize the conditions in which the scattering properties of single photons from the atom-cavity system become highly entangled with the atomic motional wave function. We also analyze the prominent observable features of this optomechanical strong coupling, which include a per-photon motional heating that is significantly larger than the single-photon recoil energy, as well as mechanically-induced oscillations in time of the second-order correlation function of the emitted light. This physics should be realizable in current experimental setups, such as trapped atoms coupled to photonic crystal cavities, and more broadly opens the door to realizing qualitatively different phenomena beyond what has been observed in optomechanical systems thus far.
Cavity optomechanics represents a frontier research direction in quantum science and technology, centered on the control and exploration of interactions between electromagnetic fields and mechanical motion. Rooted in quantum mechanics, this field realizes efficient coupling and precise manipulation of optical fields and mechanical vibrations through the structural design and precise regulation of optical microcavities and mechanical oscillators, thereby revealing and harnessing novel quantum phenomena. In recent years, cavity optomechanics has evolved into an interdisciplinary frontier integrating quantum optics, condensed matter physics, and quantum precision measurement, exhibiting profound application in both fundamental physics research and quantum information science. With advancements in technologies such as nanomanufacturing and laser cooling, optomechanical interactions have been successfully demonstrated in various experimental systems. Among these platforms, cavity cold-atom systems stand out as one of the ideal platforms for implementing quantum optomechanics. Featuring exceptional environmental isolation, long quantum coherence times, and strong light-matter interaction, these systems provide a crucial testbed for exploring strong and even ultrastrong optomechanical coupling effects as well as rich nonlinear quantum phenomena. This paper reviews the recent progress in optomechanical control and manipulation based on cavity cold-atom systems. We first outline the fundamental principles of standard cavity optomechanical systems. Then, we describe the experimental realization of linear and nonlinear optomechanical couplings in cold-atom systems. After that, we focus on the representative applications of this platform in high-precision quantum sensing, quantum memory, and the preparation of macroscopic nonclassical states. Finally, we give an outlook and challenges in this field.
We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.
The investigation of macroscopic quantum phenomena is a current active area of research that offers significant promise to advance the forefronts of both fundamental and applied quantum science. Utilising the exquisite precision and control of quantum optics provides a powerful toolset for generating such quantum states where the types and 'size' of the states that can be generated are set by the experimental parameter regime available and the resourcefulness of the protocol applied. In this work we present a new multistep scheme to 'grow' macroscopic superposition states of motion of a mechanical oscillator via cavity quantum optomechanics. The scheme consists of a series of optical pulses interacting with a mechanical mode via radiation-pressure followed by photon-counting measurements. The multistep nature of our protocol allows macroscopic superposition states to be prepared with a relaxed requirement for the single-photon optomechanical coupling strength. To illustrate the experimental feasibility of our proposal, we quantify how initial mechanical thermal occupation and mechanical decoherence affects the non-classicality and macroscopicity of the states generated and show that our scheme is resilient to optical loss. The advantages of this protocol provide a promising path to grow non-classical mechanical quantum states to a macroscopic scale under realistic experimental conditions.