We consider the dynamical behavior of a nanomechanical mirror in a high-quality cavity under the action of a coupling laser and a probe laser. We demonstrate the existence of the analog of electromagnetically induced transparency (EIT) in the output field at the probe frequency. Our calculations show explicitly the origin of EIT-like dips as well as the characteristic changes in dispersion from anomalous to normal in the range where EIT dips occur. Remarkably the pump-probe response for the optomechanical system shares all the features of the Λ system as discovered by Harris and collaborators.PACS numbers: 42.50. Gy,42.50.Wk Since its original discovery in the context of atomic vapors, electromagnetically induced transparency (EIT) [1][2][3] has been at the center of many important developments in optical physics [4] and has led to many different applications, most notably in the context of slow light [5][6][7] and the production of giant nonlinear effects. EIT is helping the progress towards studying nonlinear optics at the single-photon level. EIT has been reported in many other systems [8]. More recently, EIT has been discovered in meta materials [9][10][11][12] where resonant structures can be fabricated to correspond to dark and bright modes. Resonators provide certain advantages [13] because by design we can manipulate EIT to produce desired transmission properties of a structure. It would thus be especially interesting to study resonators coupled to other systems such as cavity optomechanical systems. Such nanomechanical systems have attracted considerable interest recently [14][15][16][17][18][19][20][21]. In this letter, we demonstrate the possibility of EIT in the context of cavity optomechanics. Before discussing our model and results, we set the stage for EIT in cavity optomechanics. As in typical EIT experiments [1][2][3][4], for example, in the context of atomic vapors, we need to examine the pump-probe response of a nanomechanical oscillator of frequency ω m coupled to a high-quality cavity via radiation pressure effects [22,23] as schematically shown in Fig. 1. Thus, the cavity oscillator of frequency ω 0 and the nano-oscillator interact nonlinearly with each other. The system is driven by a strong pump field of frequency ω c . This is the coupling field. The probe field has frequency ω p and is much weaker than the pump field. The mechanical oscillator's damping is much smaller than that of the cavity oscillator. This is very important for considerations of EIT. The decay rate of the mechanical oscillator plays the same role as the decay rate of the ground-state coherence in EIT experiments. The analog of the two-photon resonance condition where EIT occurs would be ω c + ω m = ω p . We show how the absorptive and dispersive responses of the probe change by the coupling field and how EIT emerges. We present a clear physical origin of EIT in such a system.Let us denote the cavity annihilation (creation) operator by c (c † ) with the commutation relation [c, c † ] = 1.The momentum and position o...

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We theoretically demonstrate the possibility of using nano mechanical systems as single photon routers. We show how electromagnetically induced transparency (EIT) in cavity optomechanical systems can be used to produce a switch for a probe field in a single photon Fock state using very low pumping powers of a few microwatts. We present estimates of vacuum and thermal noise and show that the optimal performance of the single photon switch is deteriorated by only a few percent even at temperatures of the order of 20 mK.PACS numbers: 42.50. Wk, 03.67.Hk, 42.50.Gy It is well known that the building of all optical devices requires strong interactions between radiation and matter as photons by themselves do not interact. One of the enabling technologies, in the context of quantum control, is the design of an optical switch or a photon router operating at a single photon level. In quantum information science one would like to distribute information over large distances. Photons are important candidates for such purposes as they can travel over long distances without much decoherence. Further, it is known that many quantum information protocols such as quantum cryptography [1] and quantum networks [2] require single photons. We need to route the photons, as different nodes in the networks have to be linked [2]. Further the routing has to be done in a way so that the state of the photon is not affected. Several proposals have been made for the realization of an optical switch-In an early work Harris and Yamamoto [3] had suggested how quantum interference can be used to operate a switch. More recently atomic EIT with cavity fields has been suggested to realize an optical switch. Single atom EIT in a cavity has been realized by using very strong atom cavity interactions [4]. Further, even vacuum induced transparency has been observed [5]. Other proposals on a photon switch are based on using a single atom in a strongly coupled waveguide array [6] and using strongly coupled atoms via surface plasmons on a nanowire [7]. There are also reports of single photon switch at telecom wavelengths using strong cross phase modulation [8] and in the microwave domain using a superconducting transmon qubit [9]. It is now known that the optomechanical systems exhibit an analog of EIT [10] which has been observed in several experiments [11]. Herein, we show how nanomechanical mirrors (NMM) in optical cavities can be used to build single photon routers (i.e. single photon switches). For this purpose we use a configuration in which the NMM is in the middle of a cavity which is bounded by two high quality mirrors [12,13]. In a Fabry-Perot cavity a single photon will be transmitted if its frequency is on resonance with the cavity. Now we drive the cavity with a strong control field which is red detuned from the cavity resonance. In the presence of the strong control field, the NMM leads to reflection of the single photon. Thus the driving field switches the route of the single probe photon. This is in contrast to the situation where one use...

It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature 300 K to sub-Kelvin temperatures, which is much lower than what is achievable in the absence of the parametric amplifier. Further if in case of a precooled mirror one can reach millikelvin temperatures starting with about 1 K. Our work demonstrates the fundamental dependence of radiation pressure effects on photon statistics. PACS numbers: 42.50.Lc, 03.65.Ta, 05.40.-a I. INTRODUCTIONRecently there is considerable interest in micromechanical mirrors. These are macroscopic quantum mechanical systems and the important question is how to reach their quantum characteristics [1][2][3][4]. The thermal noise limits many highly sensitive optical measurements [5,6]. We also note that there has been considerable interest in using micromirrors for producing superpositions of macroscopic quantum states if such micromirrors can be cooled to their quantum ground states [7,8]. Thus cooling of micromechanical resonators becomes a necessary prerequisite for all such studies. So far two different ways to cool a mechanical resonator mode have been proposed. One is active feedback scheme [9][10][11][12], where a viscous force is fed back to the movable mirror to decrease its Brownian motion.

We report electromagnetically induced transparency (EIT) using quantized fields in optomechanical systems. The weak probe field is a narrowband squeezed field. We present a homodyne detection of EIT in the output quantum field. We find that the EIT dip exists even though the photon number in the squeezed vacuum is at the single-photon level. The EIT with quantized fields can be seen even at temperatures on the order of 100 mK, thus paving the way for using optomechanical systems as memory elements.