The photon blockade effect in optomechanical systems

We analyze the photon statistics of a weakly driven optomechanical system and discuss the effect of photon blockade under single photon strong coupling conditions. We present an intuitive interpretation of this effect in terms of displaced oscillator states and derive analytic expressions for the cavity excitation spectrum and the two photon correlation function $g^{(2)}(0)$. Our results predict the appearance of non-classical photon correlations in the combined strong coupling and sideband resolved regime, and provide a first detailed understanding of photon-photon interactions in strong coupling optomechanics

Dynamical generation of synthetic electric fields for photons in the quantum regime

Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields in the minimal setup of two optical modes coupled by phonon-assisted tunneling where the phonon mode is undergoing self-oscillations. We use the quantum van-der-Pol oscillator as the simplest dynamical model for a mechanical self-oscillator that allows us to perform quantum master equation simulations. We identify a single parameter, which controls the strength of quantum fluctuations, enabling us to investigate the classical-to-quantum crossover. We show that the generation of synthetic electric fields is robust against noise and that it leads to unidirectional transport of photons also in the quantum regime, albeit with a reduced isolation ratio. Our study opens the path for studying dynamical gauge fields in the quantum regime based on optomechanical arrays

Single-photon Optomechanics

Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady-states of the mechanical oscillator when multi-photon transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.Comment: 4 pages, 4 figure

Acting Autonomously or Mimicking the State and Peers? A Panel Tobit Analysis of Financial Dependence and Aid Allocation by Swiss NGOs

NGO aid is still widely believed to be superior to official aid (ODA). However, the incentives of NGOs to excel and target aid to the poor and deserving are increasingly disputed. We contribute to the emerging literature on the allocation of NGO aid by performing panel Tobit estimations for Swiss NGOs. The analysis offers new insights in two major regards: First, we cover the allocation of both self-financed and officially co-financed aid for a large panel of NGOs and recipient countries. Second, by classifying each NGO according to its financing structure, we address the unresolved question of whether financial dependence on the government impairs the targeting of NGO aid. It turns out that NGOs mimic the state as well as NGO peers. Officially refinanced NGOs are more inclined to imitate the allocation of ODA. However, the degree of financial dependence does not affect the poverty orientation of NGO aid and the incentives of NGOs to engage in easier environments. The allocation of self-financed aid differs in several respects from the allocation of officially co-financed aid, including the role of financial dependence for imitating the state and herding among NGOs

Lifting the Franck-Condon blockade in driven quantum dots

Electron-vibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as Franck-Condon blockade and can be traced back to an overlap integral between vibron states with different electron numbers which becomes exponentially small for large electron-vibron coupling strength. Here, we investigate the effect of a time-dependent drive on this phenomenon, in particular the effect of an oscillatory gate voltage acting on the electronic dot level. We employ two different approaches: perturbation theory based on nonequilibrium Keldysh Green's functions and a master equation in Born-Markov approximation. In both cases, we find that the drive can lift the blockade by exciting vibrons. As a consequence, the relative change in average current grows exponentially with the drive strength.S.W. acknowledges financial support by the Marie Curie ITN cQOM and the ERC OPTOMECH. P.H. and T.L.S. are supported by the National Research Fund Luxembourg (ATTRACT 7556175). A.N. holds a University Research Fellowship from the Royal Society and acknowledges support from the Winton Programme for the Physics of Sustainability

Acting Autonomously or Mimicking the State and Peers? A Panel Tobit Analysis of Financial Dependence and Aid Allocation by Swiss NGOs

NGO aid is still widely believed to be superior to official aid (ODA). However, the incentives of NGOs to excel and target aid to the poor and deserving are increasingly disputed. We contribute to the emerging literature on the allocation of NGO aid by performing panel Tobit estimations for Swiss NGOs. The analysis offers new insights in two major regards: First, we cover the allocation of both self-financed and officially co-financed aid for a large panel of NGOs and recipient countries. Second, by classifying each NGO according to its financing structure, we address the unresolved question of whether financial dependence on the government impairs the targeting of NGO aid. It turns out that NGOs mimic the state as well as NGO peers. Officially refinanced NGOs are more inclined to imitate the allocation of ODA. However, the degree of financial dependence does not affect the poverty orientation of NGO aid and the incentives of NGOs to engage in easier environments. The allocation of self-financed aid differs in several respects from the allocation of officially co-financed aid, including the role of financial dependence for imitating the state and herding among NGOs

Lifting the Franck-Condon blockade in driven quantum dots

Electron-vibron coupling in quantum dots can lead to a strong suppression of the average current in the sequential tunneling regime. This effect is known as Franck-Condon blockade and can be traced back to an overlap integral between vibron states with different electron numbers which becomes exponentially small for large electron-vibron coupling strength. Here, we investigate the effect of a time-dependent drive on this phenomenon, in particular the effect of an oscillatory gate voltage acting on the electronic dot level. We employ two different approaches: perturbation theory based on nonequilibrium Keldysh Green's functions and a master equation in Born-Markov approximation. In both cases, we find that the drive can lift the blockade by exciting vibrons. As a consequence, the relative change in average current grows exponentially with the drive strength.S.W. acknowledges financial support by the Marie Curie ITN cQOM and the ERC OPTOMECH. P.H. and T.L.S. are supported by the National Research Fund Luxembourg (ATTRACT 7556175). A.N. holds a University Research Fellowship from the Royal Society and acknowledges support from the Winton Programme for the Physics of Sustainability

Full counting statistics of heteronuclear molecules from Feshbach-assisted photo association

We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation [Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities with sum frequency generation and using quantum optics methods we consider the cases where the molecules are formed from atoms out of two Bose-Einstein condensates, out of a Bose-Einstein condensate and a gas of degenerate fermions, and out of two degenerate Fermi gases with and without superfluidity. Bosons are treated in a single mode approximation and fermions in a degenerate model. In these approximations we can numerically solve the master equations describing the system's dynamics and thus we find the full counting statistics of the molecular modes. The full quantum dynamics calculations are complemented by mean field calculations and short time perturbative expansions. While the molecule production rates are very similar in all three cases at this level of approximation, differences show up in the counting statistics of the molecular fields. The intermediate field of closed-channel molecules is for short times second-order coherent if the molecules are formed from two Bose-Einstein condensates or a Bose-Fermi mixture. They show counting statistics similar to a thermal field if formed from two normal Fermi gases. The coherence properties of molecule formation in two superfluid Fermi gases are intermediate between the two previous cases. In all cases the final field of deeply-bound molecules is found to be twice as noisy as that of the intermediate state. This is a consequence of its coupling to the lossy optical cavity in our model, which acts as an input port for quantum noise, much like the situation in an optical beam splitter.Comment: replacement of earlier manuscript cond-mat/0508080 ''Feshbach-assisted photoassociation of ultracold heteronuclear molecules'' with minor revision

Two-Tone Optomechanical Instability and Its Fundamental Implications for Backaction-Evading Measurements

While quantum mechanics imposes a fundamental limit on the precision of interferometric measurements of mechanical motion due to measurement backaction, the nonlinear nature of the coupling also leads to parametric instabilities that place practical limits on the sensitivity by limiting the power in the interferometer. Such instabilities have been extensively studied in the context of gravitational wave detectors, and their presence has recently been reported in Advanced LIGO. Here, we observe experimentally and describe theoretically a new type of optomechanical instability that arises in two-tone backaction-evading (BAE) measurements, designed to overcome the standard quantum limit, and demonstrate the effect in the optical domain with a photonic crystal nanobeam, and in the microwave domain with a micromechanical oscillator coupled to a microwave resonator. In contrast to the well-known oscillatory parametric instability that occurs in single-tone, blue-detuned pumping, which is characterized by a vanishing effective mechanical damping, the parametric instability in balanced two-tone optomechanics is exponential, and is a result of small detuning errors in the two pump frequencies. Its origin can be understood in a rotating frame as the vanishing of the effective mechanical frequency due to an optical spring effect. Counterintuitively, the instability occurs even in the presence of perfectly balanced intracavity fields, and can occur for both signs of detuning. We find excellent quantitative agreement with our theoretical predictions. Since the constraints on tuning accuracy become stricter with increasing probe power, it imposes a fundamental limitation on BAE measurements, as well as other two-tone schemes. In addition to introducing a new limitation in two-tone BAE measurements, the results also introduce a new type of nonlinear dynamics in cavity optomechanics

Continuous mode cooling and phonon routers for phononic quantum networks

We study the implementation of quantum state transfer protocols in phonon networks, where in analogy to optical networks, quantum information is transmitted through propagating phonons in extended mechanical resonator arrays or phonon waveguides. We describe how the problem of a non-vanishing thermal occupation of the phononic quantum channel can be overcome by implementing optomechanical multi- and continuous mode cooling schemes to create a 'cold' frequency window for transmitting quantum states. In addition, we discuss the implementation of phonon circulators and switchable phonon routers, which rely on strong coherent optomechanical interactions only, and do not require strong magnetic fields or specific materials. Both techniques can be applied and adapted to various physical implementations, where phonons coupled to spin or charge based qubits are used for on-chip networking applications.Comment: 33 pages, 8 figures. Final version, a few minor changes and updated reference