Anticipated reward magnitude and probability comprise dual components of expected value (EV), a cornerstone of economic and psychological theory. However, the neural mechanisms that compute EV have not been characterized. Using event-related functional magnetic resonance imaging, we examined neural activation as subjects anticipated monetary gains and losses that varied in magnitude and probability. Group analyses indicated that, although the subcortical nucleus accumbens (NAcc) activated proportional to anticipated gain magnitude, the cortical mesial prefrontal cortex (MPFC) additionally activated according to anticipated gain probability. Individual difference analyses indicated that, although NAcc activation correlated with self-reported positive arousal, MPFC activation correlated with probability estimates. These findings suggest that mesolimbic brain regions support the computation of EV in an ascending and distributed manner: whereas subcortical regions represent an affective component, cortical regions also represent a probabilistic component, and, furthermore, may integrate the two.

Converting low-frequency electrical signals into much higher frequency optical signals has enabled modern communications networks to leverage both the strengths of microfabricated electrical circuits and optical fiber transmission, allowing information networks to grow in size and complexity. A microwave-to-optical converter in a quantum information network could provide similar gains by linking quantum processors via low-loss optical fibers and enabling a large-scale quantum network. However, no current technology can convert low-frequency microwave signals into high-frequency optical signals while preserving their fragile quantum state. For this demanding application, a converter must provide a near-unitary transformation between different frequencies; that is, the ideal transformation is reversible, coherent, and lossless. Here we demonstrate a converter that reversibly, coherently, and efficiently links the microwave and optical portions of the electromagnetic spectrum. We use our converter to transfer classical signals between microwave and optical light with conversion efficiencies of ∼10%, and achieve performance sufficient to transfer quantum states if the device were further precooled from its current 4 kelvin operating temperature to below 40 millikelvin. The converter uses a mechanically compliant membrane to interface optical light with superconducting microwave circuitry, and this unique combination of technologies may provide a way to link distant nodes of a quantum information network. IntroductionModern communication networks manipulate information at several gigahertz with microprocessors and distribute information at hundreds of terahertz via optical fibers. A similar frequency dichotomy is developing in quantum information processing. Superconducting qubits operating at several gigahertz have recently emerged as promising high-fidelity and intrinsically scalable quantum processors [1][2][3]. Conversely, optical frequencies provide access to low-loss transmission [4] and long-lived quantum-compatible storage [5,6]. Converting information between gigahertz-frequency "microwave light" that can be deftly manipulated and terahertzfrequency "optical light" that can be efficiently distributed will enable small-scale quantum systems [7][8][9] to be combined into larger, fully-functional quantum networks [10,11]. But no current technology can transform information between these vastly different frequencies while preserving the fragile quantum state of the information. For this demanding application, a frequency converter must provide a near-unitary transformation between microwave light and optical light; that is, the ideal transformation is reversible, coherent, and lossless.Certain nonlinear materials provide a link between microwave and optical light, and these are commonly used in electro-optic modulators (EOMs) for just this purpose. While EOMs might be capable of reversible frequency conversion [12,13], such conversion has not yet been demonstrated, and even optimized EOMs [14,15] have predicted ...

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of 1.7 +/- 0.2 dB below the shot noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.Comment: 12 pages, 8 figure

The quantum mechanics of position measurement of a macroscopic object is typically inaccessible because of strong coupling to the environment and classical noise. In this work, we monitor a mechanical resonator subject to an increasingly strong continuous position measurement and observe a quantum mechanical back-action force that rises in accordance with the Heisenberg uncertainty limit. For our optically based position measurements, the back-action takes the form of a fluctuating radiation pressure from the Poisson-distributed photons in the coherent measurement field, termed radiation pressure shot noise. We demonstrate a back-action force that is comparable in magnitude to the thermal forces in our system. Additionally, we observe a temporal correlation between fluctuations in the radiation force and in the position of the resonator.

An optical network of superconducting quantum bits (qubits) is an appealing platform for quantum communication and distributed quantum computing, but developing a quantum-compatible link between the microwave and optical domains remains an outstanding challenge. Operating at T < 100 mK temperatures, as required for quantum electrical circuits, we demonstrate a mechanically-mediated microwave-optical converter with 47% conversion efficiency, and use a classical feedforward protocol to reduce added noise to 38 photons. The feedforward protocol harnesses our discovery that noise emitted from the two converter output ports is strongly correlated because both outputs record thermal motion of the same mechanical mode. We also discuss a quantum feedforward protocol that, given high system efficiencies, would allow quantum information to be transferred even when thermal phonons enter the mechanical element faster than the electro-optic conversion rate. arXiv:1712.06535v2 [quant-ph]

The radiation pressure of light can act to damp and cool the vibrational motion of a mechanical resonator. In understanding the quantum limits of this cooling, one must consider the effect of shot noise fluctuations on the final thermal occupation. In optomechanical sideband cooling in a cavity, the finite Stokes Raman scattering defined by the cavity linewidth combined with shot noise fluctuations dictates a quantum backaction limit, analogous to the Doppler limit of atomic laser cooling. In our work we sideband cool to the quantum backaction limit by using a micromechanical membrane precooled in a dilution refrigerator. Monitoring the optical sidebands allows us to directly observe the mechanical object come to thermal equilibrium with the optical bath.

The temperature dependence of the asymmetry between Stokes and anti-Stokes Raman scattering can be exploited for self-calibrating, optically-based thermometry. In the context of cavity optomechanics, we observe the cavity-enhanced scattering of light interacting with the standingwave drumhead modes of a Si3N4 membrane mechanical resonator. The ratio of the amplitude of Stokes to anti-Stokes scattered light is used to measure temperatures of optically-cooled mechanical modes down to the level of a few vibrational quanta. We demonstrate that the Raman-ratio technique is able to measure the physical temperature of our device over a range extending from cryogenic temperatures to within an order of magnitude of room temperature.Raman light scattering has proven to be a robust and powerful technique for in situ thermometry. Many material-specific properties governing Raman transitions, such as the Stokes shift, spectral linewidth, and scattering rate vary with temperature. However, for all Raman systems the ratio of spontaneously scattered Stokes versus anti-Stokes photons is a direct measure of the initial population of the motional state. For example, at zero temperature the process of anti-Stokes scattering, which attempts to lower the motional state below the ground state, is entirely suppressed, whereas the Stokes scattering, which raises the motional state, is allowed. For thermally occupied states, an absolute, self-calibrating temperature measurement is possible by measuring this asymmetry in Raman scattering. Distributed optical fiber sensors [1] and solid state systems [2-4] make use of spontaneous Raman scattering between optical phonon levels for temperature measurements, and combustion chemistry diagnostics use rotational-vibrational molecular levels in a similar fashion [5]. Ultracold trapped ions [6,7] and neutral atoms [8,9] employ motional Raman sideband spectroscopy to reveal thermal occupations near the quantum ground state. Recent experiments in the field of quantum cavity optomechanics [10][11][12] use cavity enhancement to collect Raman-scattered light from localized acoustic resonances demonstrating the Stokes/anti-Stokes asymmetry.Here we measure the asymmetry of Raman scattering from a single, resonant laser tone driving a membranein-cavity optomechanical system (Fig. 1). The motional states are the MHz frequency vibrational levels of a membrane mechanical resonator, and an optical resonance is provided by an optical cavity surrounding the membrane. The asymmetry becomes more pronounced in certain mechanical normal modes of the resonator when they are optically cooled near their ground state with a separate laser tone. We use these measurements to verify that the damped displacement spectral density near the membrane resonance frequency is equal to that expected from a resonator occupied withn ∼ 2 vibrational quanta (∼150 µK effective temperature). Additionally, we measure the physical temperature of our device by extrapolating the Raman sideband asymmetry to zero optical damping. These measur...

We describe a cryogenic cavity-optomechanical system that combines Si 3 N 4 membranes with a mechanically rigid Fabry-Perot cavity. The extremely high products of quality factor and frequency of the membranes allow us to cool a MHz mechanical mode to a phonon occupation ofn < 10, starting at a bath temperature of 5 K. We show that even at cold temperatures thermally occupied mechanical modes of the cavity elements can be a limitation, and we discuss methods to reduce these effects sufficiently for achieving ground state cooling. This promising new platform should have versatile uses for hybrid devices and searches for radiation pressure shot noise. 11 Appendix A. Calculation of thermo-mechanical noise in an optomechanical system 11 Appendix B. Calibration of membrane motion 14 References 16