The Power of Unentanglement

The class QMA(k). introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Does QMA(k) = QMA(2) for k ≥ 2? Can QMA(k) protocols be amplified to exponentially small error? In this paper, we make progress on all of the above questions. * We give a protocol by which a verifier can be convinced that a 3SAT formula of size m is satisfiable, with constant soundness, given Õ (√m) unentangled quantum witnesses with O(log m) qubits each. Our protocol relies on the existence of very short PCPs. * We show that assuming a weak version of the Additivity Conjecture from quantum information theory, any QMA(2) protocol can be amplified to exponentially small error, and QMA(k) = QMA(2) for all k ≥ 2. * We prove the nonexistence of "perfect disentanglers" for simulating multiple Merlins with one

Critical dislocation speed in helium-4 crystals

Our experiments show that in $^4$He crystals, the binding of $^3$He impurities to dislocations does not necessarily imply their pinning. Indeed, in these crystals, there are two different regimes of the motion of dislocations when impurities bind to them. At lowdriving strain $\epsilon$ and frequency $\omega$, where the dislocation speed is less than a critical value (45 $\mu$m/s), dislocations and impurities apparently move together. Impurities really pin the dislocations only at higher values of $\omega$. The critical speed separating the two regimes is two orders of magnitude smaller than the average speed of free $^3$He impurities in the bulk crystal lattice.We obtained this result by studying the dissipation of dislocation motion as a function of the frequency and amplitude of a driving strain applied to a crystal at low temperature. Our results solve an apparent contradiction between some experiments, which showed a frequency-dependent transition temperature from a soft to a stiff state, and other experiments or models where this temperature was assumed to be independent of frequency. The impurity pinning mechanism for dislocations appears to be more complicated than previously assumed

Strong gate coupling of high-Q nanomechanical resonators

The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends towards zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2 \pi) 1 MHz/nm for metallic beam resonators at tens of MHz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electrodes, in suspended aluminum films. We measured the thermomechanical vibrations down to a temperature of 25 mK, and we obtained a low number of about twenty phonons at the equilibrium bath temperature. The mechanical properties of Al were excellent after FIB cutting and we recorded a quality factor of Q ~ 3 x 10^5 for a 67 MHz resonator at a temperature of 25 mK. Between 0.2K and 2K we find that the dissipation is linearly proportional to the temperature.Comment: 6 page

Classical decoherence in a nanomechanical resonator

SI not providedInternational audienceDecoherence is an essential mechanism that defines the boundary between classical and quantum behaviours, while imposing technological bounds for quantum devices. Little is known about quantum coherence of mechanical systems, as opposed to electromagnetic degrees of freedom. But decoherence can also be thought of in a purely classical context, as the loss of phase coherence in the classical phase space. Indeed the bridge between quantum and classical physics is under intense investigation, using classical nanomechanical analogues of quantum phenomena. In the present work, by separating pure dephasing from dissipation, we quantitatively model the classical decoherence of a mechanical resonator: through the experimental control of frequency fluctuations, we engineer artificial dephasing. We report on the methods available to define pure dephasing in these systems, which are prerequisite in the understanding of decoherence processes in mechanical devices, both classical and quantum

Fully suspended nano-beams for quantum fluids

Non-invasive probes are keystones of fundamental research. Their size, and maneuverability (in terms of e.g. speed, dissipated power) define their applicability range for a specific use. As such, solid state physics possesses e.g. Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), or Scanning SQUID Microscopy. In comparison, quantum fluids (superfluid $^3$He, $^4$He) are still lacking probes able to sense them (in a fully controllable manner) down to their smallest relevant lengthscales, namely the coherence length $\xi_0$. In this work we report on the fabrication and cryogenic characterization of fully suspended (hanging over an open window, with no substrate underneath) Si$_3$N$_4$ nano-beams, of width down to 50 nm and quality factor up to $10^5$. As a benchmark experiment we used them to investigate the Knudsen boundary layer of a rarefied gas: $^4$He at very low pressures. The absence of the rarefaction effect due to the nearby chip surface discussed in Gazizulin et al. [1] is attested, while we report on the effect of the probe size itself

The thermal conductivity of silicon nitride membranes is not sensitive to stress

We have measured the thermal properties of suspended membranes from 10 K to 300 K for two amplitudes of internal stress (about 0.1 GPa and 1 GPa) and for two different thicknesses (50 nm and 100 nm). The use of the original 3 \omega -Volklein method has allowed the extraction of both the specific heat and the thermal conductivity of each SiN membrane over a wide temperature range. The mechanical properties of the same substrates have been measured at helium temperatures using nanomechanical techniques. Our measurements show that the thermal transport in freestanding SiN membranes is not affected by the presence of internal stress. Consistently, mechanical dissipation is also unaffected even though Qs increase with increasing tensile stress. We thus demonstrate that the theory developed by Wu and Yu [Phys. Rev. B 84, 174109 (2011)] does not apply to this amorphous material in this stress range. On the other hand, our results can be viewed as a natural consequence of the "dissipation dilution" argument [Y. L. Huang and P. R. Saulson, Rev. Sci. Instrum. 69, 544 (1998)] which has been introduced in the context of mechanical damping.Comment: 15 pages, 6 figures. Submitted to PR

Nano-beam clamping revisited

Within recent years, the field of nano-mechanics has diversified in a variety of applications, ranging from quantum information processing to biological molecules recognition. Among the diversity of devices produced these days, the simplest (but versatile) element remains the doubly-clamped beam: it can store very large tensile stresses (producing high resonance frequencies $f_0$ and quality factors $Q$), is interfaceable with electric setups (by means of conductive layers), and can be produced easily in clean rooms (with scalable designs including multiplexing). Besides, its mechanical properties are the simplest to describe. Resonance frequencies and $Q$s are being modeled, with as specific achievement the ultra-high quality resonances based on ``soft clamping'' and ``phonon shields''. Here, we demonstrate that the fabrication undercut of the clamping regions of basic nano-beams produces a ``natural soft clamping'', given for free. We present the analytic theory that enables to fit experimental data, which can be used for $\{ Q , f_0 \}$ design.Comment: With Supplementary Informatio

Measuring frequency fluctuations in nonlinear nanomechanical resonators

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive up to date. In this Letter we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly-clamped beams, in a cryogenic environment. We report on the same $T/f$ dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected {\it damping fluctuations}, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing, and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure $\delta f/f_0$ lies in the range $0.5 - 0.01~$ppm (consistent with literature for cryogenic MHz devices), and decreases with mode number in the range studied. The technique can be applied to {\it any types} of nano-mechanical structures, enabling progresses towards the understanding of intrinsic sources of noise in these devices.Comment: Published 7 may 201

Very low resistance Al/Cu joints for use at cryogenic temperatures

We present two different techniques for achieving low resistance ($<$20 n$\rm \Omega$) contacts between copper and aluminium at cryogenic temperatures. The best method is based on gold plating of the surfaces in an e-beam evaporator immediately after Ar plasma etching in the same apparatus, yielding resistances as low as 3 n$\rm \Omega$ that are stable over time. The second approach involves inserting indium in the Al/Cu joint. For both methods, we believe key elements are surface polishing, total removal of the aluminum oxide surface layer, and temporary application of large (typ. 11 kN) compression forces. We believe the values for gold plated contacts are the lowest ever reported for a Cu/Al joint of a few $\rm cm^{2}$. This technology could simplify the construction of thermal links for advanced cryogenics applications, in particular that of extremely low resistance heat switches for nuclear demagnetization refrigerators.Comment: Accepted by Journal of Low Temperature Physic

High-Q silicon nitride drum resonators strongly coupled to gates

Silicon nitride (SiN) mechanical resonators with high quality mechanical properties are attractive for fundamental research and applications. However, it is challenging to maintain these mechanical properties while achieving strong coupling to an electrical circuit for efficient on-chip integration. Here, we present a SiN drum resonator covered with an aluminum thin film, enabling large capacitive coupling to a suspended top-gate. Implementing the full electrical measurement scheme, we demonstrate a high quality factor ~ 1E4 (comparable to that of bare drums at room temperature) and present our ability to detect ? 10 mechanical modes at low temperature. The drum resonator is also coupled to a microwave cavity, so that we can perform optomechanical sideband pumping with a fairly good coupling strength G and demonstrate mechanical parametric amplification. This SiN drum resonator design provides efficient electrical integration and exhibits promising features for exploring mode coupling and signal processing