Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction (original) (raw)

Macroscopic mechanical oscillators at the quantum limit through optomechanical cooling

Journal of the Optical Society of America B, 2003

We discuss how the optomechanical coupling provided by radiation pressure can be used to cool macroscopic collective degrees of freedom, as vibrational modes of movable mirrors. Cooling is achieved using a phase-sensitive feedback-loop which effectively overdamps the mirrors motion without increasing the thermal noise. Feedback results able to bring macroscopic objects down to the quantum limit. In particular, it is possible to achieve squeezing and entanglement.

Radiation Pressure Cooling as a Quantum Dynamical Process

Physical review letters, 2017

One of the most fundamental problems in optomechanical cooling is how small the thermal phonon number of a mechanical oscillator can be achieved under the radiation pressure of a proper cavity field. Different from previous theoretical predictions, which were based on an optomechanical system's time-independent steady states, we treat such cooling as a dynamical process of driving the mechanical oscillator from its initial thermal state, due to its thermal equilibrium with the environment, to a stabilized quantum state of higher purity. We find that the stabilized thermal phonon number left in the end actually depends on how fast the cooling process could be. The cooling speed is decided by an effective optomechanical coupling intensity, which constitutes an essential parameter for cooling, in addition to the sideband resolution parameter that has been considered in other theoretical studies. The limiting thermal phonon number that any cooling process cannot surpass exhibits a d...

Self-cooling of a movable mirror to the ground state using radiation pressure

Physical Review A, 2008

We show that one can cool a micro-mechanical oscillator to its quantum ground state using radiation pressure in an appropriately detuned cavity (self-cooling). From a simple theory based on Heisenberg-Langevin equations we find that optimal self-cooling occurs in the good cavity regime, when the cavity bandwidth is smaller than the mechanical frequency, but still larger than the effective mechanical damping. In this case the intracavity field and the vibrational mechanical mode coherently exchange their fluctuations. We also present dynamical calculations which show how to access the mirror final temperature from the fluctuations of the field reflected by the cavity. PACS numbers: 42.50.Lc, 03.67.Mn, 05.40.Jc

Gain-tunable optomechanical cooling in a laser cavity

Physical Review A, 2013

We study the optical cooling of the cavity mirror in an active laser cavity. We find that the optical damping rate is vanishingly small for an incoherently pumped laser above threshold. In the presence of an additional external coherent drive however, the optical damping rate can be enhanced substantially with respect to that of a passive cavity. We show that the strength of the incoherent pump provides the means to tune the optical damping rate and the steady state phonon number. The system is found to undergo a transition from the weak optomechanical coupling regime to the strong optomechanical coupling regime as the strength of the incoherent pump is varied.

Ground-state cooling in cavity optomechanics with unresolved sidebands

EPL (Europhysics Letters)

We consider a simple cavity optomechanics and study the ground-state cooling of mechanical resonator in the quantum regime. Using the effective master equations in the linear regime, the equations of motion can be obtained for the second order moments. The steady state solutions are derived in the case where the antiresonant terms are ignored. The final mean value of phonon number is compared the case where the antiresonant terms are included. We find that the groundstate cooling in the last case is improved. Indeed, the inclusion of the antiresonant terms makes the system able to generate a squeezed field, which is required for enhancing cooling. The variances of the resultant field are presented. Analytic calculations are presented in some appropriate regimes. Then our analytic predictions are confirmed with numerical calculations.

Laser cooling of a nanomechanical oscillator into its quantum ground state

Nature, 2011

A patterned Si nanobeam is formed which supports co-localized acoustic and optical resonances that are coupled via radiation pressure. Starting from a bath temperature of T b ≈ 20 K, the 3.68 GHz nanomechanical mode is cooled into its quantum mechanical ground state utilizing optical radiation pressure. The mechanical mode displacement fluctuations, imprinted on the transmitted cooling laser beam, indicate that a final phonon mode occupancy ofn = 0.85 ± 0.04 is obtained.

Sideband cooling of micromechanical motion to the quantum ground state

Nature, 2011

The advent of laser cooling techniques revolutionized the study of many atomic-scale systems. This has fueled progress towards quantum computers by preparing trapped ions in their motional ground state [1], and generating new states of matter by achieving Bose-Einstein condensation of atomic vapors [2]. Analogous cooling techniques [3, 4] provide a general and flexible method for preparing macroscopic objects in their motional ground state, bringing the powerful technology of micromechanics into the quantum regime. Cavity optoor electro-mechanical systems achieve sideband cooling through the strong interaction between light and motion [5][6][7][8][9][10][11][12]. However, entering the quantum regime, less than a single quantum of motion, has been elusive because sideband cooling has not sufficiently overwhelmed the coupling of mechanical systems to their hot environments. Here, we demonstrate sideband cooling of the motion of a micromechanical oscillator to the quantum ground state. Entering the quantum regime requires a large electromechanical interaction, which is achieved by embedding a micromechanical membrane into a superconducting microwave resonant circuit. In order to verify the cooling of the membrane motion into the quantum regime, we perform a near quantumlimited measurement of the microwave field, resolving this motion a factor of 5.1 from the Heisenberg limit [3]. Furthermore, our device exhibits strong-coupling allowing coherent exchange of microwave photons and mechanical phonons . Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion , possibly even testing quantum theory itself in the unexplored region of larger size and mass . The universal ability to connect disparate physical systems through mechanical motion naturally leads towards future methods for engineering the coherent transfer of quantum information with widely different forms of quanta.

Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state

Phys Rev a, 2011

Cooling a mesoscopic mechanical oscillator to its quantum ground state is elementary for the preparation and control of low entropy quantum states of large scale objects. Here, we pre-cool a 70-MHz micromechanical silica oscillator to an occupancy below 200 quanta by thermalizing it with a 600-mK cold 3 He gas. Two-level system induced damping via structural defect states is shown to be strongly reduced, and simultaneously serves as novel thermometry method to independently quantify excess heating due to a cooling laser. We demonstrate that dynamical backaction sideband cooling can reduce the average occupancy to 9 ± 1 quanta, implying that the mechanical oscillator can be found (10 ± 1)% of the time in its quantum ground state.