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 BoseEinstein 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][13][14][15]. 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 [16]. 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 [17,18], possibly even testing quantum theory itself in the unexplored region of larger size and mass [19]. 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.Mechanical oscillators that are both decoupled from their environment (high quality factor Q) and placed in the quantum regime could allow us to explore quantum mechanics in entirely new ways [17][18][19][20][21]. For an oscillator to be in the quantum regime, it must be possible to prepare it in its ground state, to arbitrarily manipulate its quantum state, and to detect its state near the Heisenberg limit. In order to prepare an oscillator in its ground state, its temperature T must be reduced such that k B T < Ω m , where Ω m is the resonance frequency of the oscillator, k B is Boltzmann's constant, and is the reduced Planck's constant. While higher resonance frequency modes (> 1 GHz) can meet this cooling requirement with conventional refrigeration (T < 50 mK), these stiff oscillators are difficult to control and to detect within their short mechanical lifetimes. One unique approach using passive cooling has successfully overcome these difficulties by using a piezoelectric dilatation osci...

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 ...

1It has recently become possible to encode the quantum state of superconducting qubits and the position of nanomechanical oscillators into the states of microwave fields 1,2 . However, to make an ideal measurement of the state of a qubit, or to detect the position of a mechanical oscillator with quantum-limited sensitivity requires an amplifier that adds no noise. If an amplifier adds less than half a quantum of noise, it can also squeeze the quantum noise of the electromagnetic vacuum. Highly squeezed states of the vacuum serve as an important quantum information resource. They can be used to generate entanglement or to realize back-action-evading measurements of position 3,4 . Here we introduce a general purpose parametric device, which operates in a frequency band between 4 and 8 GHz. It is a subquantum-limited microwave amplifier, it amplifies quantum noise above the added noise of commercial amplifiers, and it squeezes quantum fluctuations by 10 dB.With the emergence of quantum information processing with electrical circuits, there is a renewed interest in Josephson parametric devices 5,6,7,8,9 . Previous work with Josephson parametric amplifiers demonstrated that they can operate with subquantum-limited added noise and modestly squeeze vacuum noise 10,11,12,13,14 . Earlier realizations of Josephson parametric amplifiers (JPAs) were only capable of amplifying signals in a narrow frequency range, were not operated with large enough gain to make the noise of the following, conventional amplifier negligible or were too lossy to be subquantum limited 5 . For related reasons, the degree of squeezing of the vacuum noise was never larger than 3 dB. We create a new type of parametric amplifier in which we embed a tunable, low-loss, and nonlinear metamaterial in a microwave cavity. The tunability of the metamaterial allows us to adjust the amplified band between 4 and 8 GHz, and the cavity isolates the gain medium from low-frequency noise, providing the stability required to achieve high gains and large squeezing.A single mode of a microwave field with angular frequency ω can be decomposed in two orthogonal components, referred to as quadratureŝ V (t) ∝X 1 cos ωt +X 2 sin ωt whereX 1 andX 2 are conjugate quantum variables obeying the commutation relation [X 1 ,X 2 ] = i/2. The proportionality constant depends on the details of the mode 15,16,17 .As a consequence of the commutation relation, the uncertainties inX 1 andX 2 are subject 2 to the Heisenberg constraint ∆X 1 ∆X 2 ≥ 1/4, where ∆X 2 j is the variance of the quadrature amplitudeX j . A mode is "squeezed" if for one of the quadratures ∆X j < 1/2 (ref. 17). An amplifier that transforms both input quadratures by multiplying them by a gain √ G must add at least half a quantum of noise for the output signal to obey the commutation relation 18 ; if it adds exactly half a quantum of noise, it is quantum limited. On the other hand, an amplifier which transforms the input signal by multiplying one quadrature by √ G and multiplying the other quadrature by 1/ √ G would...