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Physical Review A

Multiparameter optimization for ground-state cooling of a mechanical mode using quantum dots

Neelesh Kumar Vij, Harish S. Adsule, Meenakshi Khosla, Shilpi Gupta

Published Mar 7, 2024• 0 citations
Publisher

Abstract

Cooling a mechanical mode to its motional ground state opens up avenues for both scientific and technological advancements in the field of quantum metrology and information processing. We propose a multiparameter optimization scheme for ground-state cooling of a mechanical mode using quantum dots. Applying the master-equation approach, we formulate the optimization scheme over a broad range of system parameters including detunings, decay rates, pumping rates, and coupling strengths. We implement the optimization scheme on two major types of semiconductor quantum-dot systems: colloidal and epitaxial quantum dots. These systems span a broad range of mechanical-mode frequencies, coupling rates, and decay rates. Our optimization scheme lowers the steady-state phonon number in all cases by several orders of magnitude and thereby the effective temperature of the mechanical mode by more than an order of magnitude. We also calculate the net cooling rate by estimating the phonon decay rate and show that the optimized system parameters also result in efficient cooling. The proposed optimization scheme can be readily extended to other driven systems coupled to a mechanical mode.

DOI
10.1103/physreva.109.033510

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Cooling a mechanical mode to its motional ground state opens up avenues for both scientific and technological advancements in the field of quantum metrology and information processing. We propose a multiparameter optimization scheme for ground-state cooling of a mechanical mode using quantum dots. Applying the master-equation approach, we formulate the optimization scheme over a broad range of system parameters including detunings, decay rates, pumping rates, and coupling strengths. We implement the optimization scheme on two major types of semiconductor quantum-dot systems: colloidal and epitaxial quantum dots. These systems span a broad range of mechanical-mode frequencies, coupling rates, and decay rates. Our optimization scheme lowers the steady-state phonon number in all cases by several orders of magnitude and thereby the effective temperature of the mechanical mode by more than an order of magnitude. We also calculate the net cooling rate by estimating the phonon decay rate and show that the optimized system parameters also result in efficient cooling. The proposed optimization scheme can be readily extended to other driven systems coupled to a mechanical mode.
We theoretically investigate a quadratic optomechanical system comprising a single-mode optical cavity linearly coupled to one mechanical resonator and quadratically coupled to a second resonator. By tuning the cavity detuning and optomechanical coupling strengths, we demonstrate the transition from optical bistability to multistability with up to seven steady-state solutions. Notably, simultaneous ground-state cooling of both mechanical resonators occurs on the dynamically stable branch of the nonlinear steady-state solutions, offering new opportunities for combined nonlinear optical and quantum cooling functionalities. Beyond the multistable regime, we systematically study dual-mode ground-state cooling and find that robust simultaneous cooling can be achieved over a broad parameter range, except when the linear and quadratic couplings become comparable, where a dark-mode effect arises. In this case, tuning the second-order optomechanical-induced frequency shifts effectively suppresses dark-mode interference, enabling controllable and simultaneous ground-state cooling. Our results provide a versatile framework for engineering multimode quantum states in optomechanical systems and open new avenues for the development of multifunctional quantum devices, including ultra-sensitive sensors, scalable quantum memories, and integrated quantum networks.
We analyze the cooling of a mechanical resonator coupled to an ensemble of interacting two-level systems via an open quantum systems approach. Using an exact analytical result, we find optimal cooling occurs when the phonon mode is critically coupled $(\ensuremath{\gamma}\ensuremath{\sim}g)$ to the two-level system ensemble. Typical systems operate in suboptimal cooling regimes due to the intrinsic parameter mismatch $(\ensuremath{\gamma}\ensuremath{\gg}g)$ between the dissipative decay rate $\ensuremath{\gamma}$ and the coupling factor ggg. To overcome this obstacle, we show that carefully engineering the coupling parameters through the strain profile of the mechanical resonator allows phonon cooling to proceed through the dark (subradiant) entangled states of an interacting ensemble, thereby resulting in optimal phonon cooling. Our results provide an avenue for ground-state cooling and should be accessible for experimental demonstrations.
Abstract We propose a ground state cooling scheme for an optomechanical resonator based on the system of a V-type three-level QD ensemble trapped in a two-mode cavity. The two-mode cavity was pumped by two different deriving fields. We studied the optomechanical cooling under the highly unresolved-sideband and beyond Lamb-Dicke regime (coupling strength between the cavity field and the phonon field not far less than the vibrational frequency). Our results show that the noise spectrum appeared a single peak when the detuning of the QD’s high excitation state and high-frequency driving field equals that of the QD’s low excitation state and low-frequency driving field, otherwise, then appeared double peaks. In the case of double peaks, we can realize the transition between optomechanical cooling and heating by changing the coupling strength of QD with cavity field, which is not available in the case of a single peak. We also studied the evolution of the mean phonon number with time, which is helpful to analyze ground state optomechanical cooling.
We propose a technique that allows to laser cool a nanomechanical resonator mode to its motional ground state. The method is based on resonant laser excitation of a phonon sideband of an embedded self-assembled quantum dot. The strength of this sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot (QD) optical transition. When compared with the analogous sideband-cooling of a trapped-ion (TI), we find novel quantum interference effects in the cooling cycle and that the finite Q-value can lead to regimes where the final occupancy is proportional to the initial one -- with their ratio determined by the product of the "effective Lamb-Dicke" parameter and the Q-value. The interactions underlying this cooling scheme also provide a tool-box for quantum state engineering in these systems.
We propose a rapid ground-state optomechanical cooling scheme in a hybrid system, where a two-level quantum dot (QD) is placed in a single-mode cavity and a nanomechanical resonator (NMR) is also coupled to the cavity via radiation pressure. The cavity is driven by a weak laser field while the QD is driven by another weak laser field. Due to the quantum destructive interference arisen from different transition channels induced by simultaneously driving the QD-cavity system in terms of the two different lasers, two-photon absorption for the cavity field can be effectively eliminated by performing an optimal quantum interference condition. Furthermore, it is demonstrated that the QD-cavity system can be unbalancedly prepared in two single-polariton states with different eigenenergies. If the frequency of the NMR is tuned to be resonant with transition between two single-polariton states, it is found that a fast ground-state cooling for the NMR can also be achieved, even when the QD-cavity system is originally in the moderate-coupling regime. Thus the present ground-state cooling scheme for the NMR may be realized with currently available experimental technology.
Abstract Quantum manipulation of mechanical oscillators has important applications in fundamental physics and quantum information processing. Ground-state cooling of the mechanical oscillators is the prerequisite for these applications. In this paper, we propose a scheme for cooling double mechanical oscillators simultaneously, in which the parametric processes induced by a degenerate optical parameter amplifier (OPA) change the statistical properties of the cavity field, resulting in the lower average phonon numbers. However, it is worth noting that two mechanical modes with the same frequency cannot be cooled due to destructive interference between the two cooling processes. While two mechanical oscillators with different frequencies can be simultaneously cooled to near their ground-state, and the cooling efficiency can be improved by increasing the parametric gain of OPA.