Abstract
Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we find that in ultrahigh vacuum quantum squeezing is achievable at room temperature with feedback cooling. For moderate vacuum, quantum squeezing is possible with cryogenic temperature. Second, we present a setup for two mechanical modes coupled to the dressed three levels, which results in two-mode squeezing analogous to the mechanism of the single-mode case. In contrast to previous works, our study provides a deterministic method for engineering macroscopic squeezed states without the requirement for a cavity.
Highlights
Optical levitation has been a powerful tool for trapping and manipulating small particles since its inception [1]
We propose a method for creating singleand two-mode squeezed states of mechanical oscillation of an optically levitated single NV center nanodiamond, motivated by the potential for the applications of such states to sensitive metrology [28]
The analysis presented using an optically levitated nanodiamond is quite general, the proposal can be extended to related systems, such as, nanodiamonds using magneto-gravitational traps [63] or Paul traps [64, 65], which avoid optical scattering, or a single NV center coupled to an cantilever [55]
Summary
Optical levitation has been a powerful tool for trapping and manipulating small particles since its inception [1]. Distinct from the works cited above [60, 61], our method does not require a measurement-based technique, but instead relies on a microwave field-induced spin-state coherence for generating steady-state mechanical squeezing in both the single-mode and two-mode cases. By applying two microwave fields coupling the |0 and |±1 states of the NV center ground-state triplet [55], a dressed three-level system is created to induce a two-phonon transition in the mechanical oscillator, an interesting effect which has not been studied before, to the best of our knowledge, in spin-optomechanical systems. To arrive at our results, we employ a master equation approach to describe the mechanical motion, by tracing out the spin degree of freedom in the Born-Markov approximation This approach is enabled by applying optically-induced dissipation [62] to the spin triplet states leading to relaxation rates much stronger than the spin-mechanical coupling. The analysis presented using an optically levitated nanodiamond is quite general, the proposal can be extended to related systems, such as, nanodiamonds using magneto-gravitational traps [63] or Paul traps [64, 65] , which avoid optical scattering, or a single NV center coupled to an cantilever [55]
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