Quantum state preparation and tomography of entangled mechanical resonators.

Precisely engineered mechanical oscillators keep time, filter signals and sense motion, making them an indispensable part of the technological landscape of today. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors1-3. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout4,5, phonon number resolution6,7 and phonon-mediated qubit-qubit interactions8,9. At present, these acoustic platforms lack processors capable of controlling the quantum states of several mechanical oscillators with a single qubit and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit-mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the phonon number distributions of the resonators by means of Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step towards feedback-based operation of a quantum acoustic processor.

Resolving the energy levels of a nanomechanical oscillator.

The quantum nature of an oscillating mechanical object is anything but apparent. The coherent states that describe the classical motion of a mechanical oscillator do not have a well defined energy, but are quantum superpositions of equally spaced energy eigenstates. Revealing this quantized structure is only possible with an apparatus that measures energy with a precision greater than the energy of a single phonon. One way to achieve this sensitivity is by engineering a strong but nonresonant interaction between the oscillator and an atom. In a system with sufficient quantum coherence, this interaction allows one to distinguish different energy eigenstates using resolvable differences in the atom's transition frequency. For photons, such dispersive measurements have been performed in cavity1,2 and circuit quantum electrodynamics3. Here we report an experiment in which an artificial atom senses the motional energy of a driven nanomechanical oscillator with sufficient sensitivity to resolve the quantization of its energy. To realize this, we build a hybrid platform that integrates nanomechanical piezoelectric resonators with a microwave superconducting qubit on the same chip. We excite phonons with resonant pulses and probe the resulting excitation spectrum of the qubit to observe phonon-number-dependent frequency shifts that are about five times larger than the qubit linewidth. Our result demonstrates a fully integrated platform for quantum acoustics that combines large couplings, considerable coherence times and excellent control over the mechanical mode structure. With modest experimental improvements, we expect that our approach will enable quantum nondemolition measurements of phonons4 and will lead to quantum sensors and information-processing approaches5 that use chip-scale nanomechanical devices.

Arbitrary electro-optic bandwidth and frequency control in lithium niobate optical resonators.

In situ tunable photonic filters and memories are important for emerging quantum and classical optics technologies. However, most photonic devices have fixed resonances and bandwidths determined at the time of fabrication. Here we present an in situ tunable optical resonator on thin-film lithium niobate. By leveraging the linear electro-optic effect, we demonstrate widely tunable control over resonator frequency and bandwidth on two different devices. We observe up to ∼50 × tuning in the bandwidth over ∼50 V with linear frequency control of ∼230 MHz/V. We also develop a closed-form model predicting the tuning behavior of the device. This paves the way for rapid phase and amplitude control over light transmitted through our device.

Excess Heat Capacity in Mo/Au Transition Edge Sensor Bolometric Detectors.

Excess heat capacity in a bolometric detector has the consequence of increasing or leading to multiple device time constants. The Mo/Au bilayer transition edge sensor (TES) bolometric detectors initially fabricated for the high resolution mid-infrared spectrometer (HIRMES) exhibited two response thermalization scales, one of which is a few times longer than estimates based upon the properties of the bulk materials employed in the design. The relative contribution of this settling time to the overall time response of the detectors is roughly proportional to the pixel area, which ranges between ~0.3 and 2.6 mm2. Use of laser ablation to remove sections of the silicon membranes comprising the pixels results in a detector response with a smaller contribution from the secondary time constant. Additional information about the nature of this excess heat capacity is gleaned from glancing incidence x-ray diffraction, which reveals the presence of molybdenum silicides near the silicon surface which is a consequence of the bi-layer deposition. Quantitative analysis of the concentration of excess molybdenum, estimated with secondary ion mass spectroscopy, is commensurate to the additional heat capacity needed to explain the anomalous time response of the detectors.

Experimental Determination of Partitioning in the Fe-Ni System for Applications to Modeling Meteoritic Metals.

Experimental trace element partitioning values are often used to model the chemical evolution of metallic phases in meteorites, but limited experimental data were previously available to constrain the partitioning behavior in the basic Fe-Ni system. In this study, we conducted experiments that produced equilibrium solid metal and liquid metal phases in the Fe-Ni system and measured the partition coefficients of 25 elements. The results are in good agreement with values modeled from IVB iron meteorites and with the limited previous experimental data. Additional experiments with low levels of S and P were also conducted, to help constrain the partitioning behaviors of elements as a function of these light elements. The new experimental results were used to derive a set of parameterization values for element solid metal-liquid metal partitioning behavior in the Fe-Ni-S, Fe-Ni-P, and Fe-Ni-C ternary systems at 0.1 MPa. The new parameterizations require that the partitioning behaviors in the light-element-free Fe-Ni system are those determined experimentally by this study, in contrast to previous parameterizations that allowed this value to be determined as a best-fit parameter. These new parameterizations, with self-consistent values for partitioning in the end-member Fe-Ni system, provide a valuable resource for future studies that model the chemical evolution of metallic phases in meteorites.

Composite reflective/absorptive IR-blocking filters embedded in metamaterial antireflection-coated silicon.

Infrared (IR)-blocking filters are crucial for controlling the radiative loading on cryogenic systems and for optimizing the sensitivity of bolometric detectors in the far-IR. We present a new IR filter approach based on a combination of patterned frequency-selective structures on silicon and a thin (25-75 µm thick) absorptive composite based on powdered reststrahlen absorbing materials. For a 300 K blackbody, this combination reflects ∼50% of the incoming light and blocks >99.8% of the total power with negligible thermal gradients and excellent low-frequency transmission. This allows a reduction in the IR thermal loading to negligible levels in a single cold filter. These composite filters are fabricated on silicon substrates, which provide excellent thermal transport laterally through the filter and ensure that the entire area of the absorptive filter stays near the bath temperature. A metamaterial antireflection coating cut into these substrates reduces in-band reflections to below 1%, and the in-band absorption of the powder mix is below 1% for signal bands below 750 GHz. This type of filter can be directly incorporated into silicon refractive optical elements.

Spectrometer baseline control via spatial filtering.

An absorptive half-moon aperture mask is experimentally explored as a broad-bandwidth means of eliminating spurious spectral features arising from reprocessed radiation in an infrared Fourier transform spectrometer. In the presence of the spatial filter, an order of magnitude improvement in the fidelity of the spectrometer baseline is observed. The method is readily accommodated within the context of commonly employed instrument configurations and leads to a factor of two reduction in optical throughput. A detailed discussion of the underlying mechanism and limitations of the method are provided.

Studying phonon coherence with a quantum sensor.

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size ( n ¯ ≃ 1 - 10 phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

Surface modification and coherence in lithium niobate SAW resonators.

Lithium niobate is a promising material for developing quantum acoustic technologies due to its strong piezoelectric effect and availability in the form of crystalline thin films of high quality. However, at radio frequencies and cryogenic temperatures, these resonators are limited by the presence of decoherence and dephasing due to two-level systems. To mitigate these losses and increase device performance, a more detailed picture of the microscopic nature of these loss channels is needed. In this study, we fabricate several lithium niobate acoustic wave resonators and apply different processing steps that modify their surfaces. These treatments include argon ion sputtering, annealing, and acid cleans. We characterize the effects of these treatments using three surface-sensitive measurements: cryogenic microwave spectroscopy measuring density and coupling of TLS to mechanics, X-ray photoelectron spectroscopy and atomic force microscopy. We learn from these studies that, surprisingly, increases of TLS density may accompany apparent improvements in the surface quality as probed by the latter two approaches. Our work outlines the importance that surfaces and fabrication techniques play in altering acoustic resonator coherence, and suggests gaps in our understanding as well as approaches to address them.

Large-aperture wide-bandwidth antireflection-coated silicon lenses for millimeter wavelengths.

The increasing scale of cryogenic detector arrays for submillimeter and millimeter wavelength astrophysics has led to the need for large aperture, high index of refraction, low loss, cryogenic refracting optics. Silicon with n=3.4, low loss, and high thermal conductivity is a nearly optimal material for these purposes but requires an antireflection (AR) coating with broad bandwidth, low loss, low reflectance, and a matched coefficient of thermal expansion. We present an AR coating for curved silicon optics comprised of subwavelength features cut into the lens surface with a custom three-axis silicon dicing saw. These features constitute a metamaterial that behaves as a simple dielectric coating. We have fabricated silicon lenses as large as 33.4 cm in diameter with micromachined layers optimized for use between 125 and 165 GHz. Our design reduces average reflections to a few tenths of a percent for angles of incidence up to 30° with low cross polarization. We describe the design, tolerance, manufacture, and measurements of these coatings and present measurements of the optical properties of silicon at millimeter wavelengths at cryogenic and room temperatures. This coating and lens fabrication approach is applicable from centimeter to submillimeter wavelengths and can be used to fabricate coatings with greater than octave bandwidth.

Metrology of infrared superconducting bolometers with a backshort.

We present the detailed metrology of a superconducting Transition-Edge Sensor (TES) absorber-coupled bolometer array bonded to a variable-delay backshort to form an integral field unit. The backshort is shaped as a wedge to continuously vary the electrical phase delay of the bolometer absorber reflective termination across the array. This resonant absorber termination structure is used to define a spectral response over a 4:1 bandwidth in the far-infrared, from ∼30 to 120 µm. The metrology of the backshort-bolometer array hybrid was achieved with a laser confocal microscope and a compact cryogenic system that provides a well-defined thermal (radiative and conductive) environment for the hybrid when cooled to ∼10 K. The results show the backshort free-space delays do not change with cooling. The estimated backshort slope is 1.58 milli-radians and within 0.3% of the targeted value. The sources of error in the free-space delay of the hybrid and optical cryogenic metrology implementations are discussed in detail. We also present measurements of the bolometer's single-crystal silicon membrane topography. The membranes deform and deflect out-of-plane under both warm and cold conditions. Intriguingly, the optically active area of the membranes tends to flatten when cold and repeatably achieve the same mechanical state over many thermal cycles; hence, no evidence for thermally-induced mechanical instability is observed. Most of the cold deformation is sourced from thermally-induced stress in the metallic layers comprising the TES element of the bolometer pixels. These results provide important considerations for the design of ultra-low-noise TES bolometers.

Superfluid liquid helium control for the primordial inflation polarization explorer balloon payload.

The Primordial Inflation Polarization Explorer (PIPER) is a stratospheric balloon payload to measure the polarization of the cosmic microwave background. Twin telescopes mounted within an open-aperture bucket dewar couple the sky to bolometric detector arrays. We reduce detector loading and photon noise by cooling the entire optical chain to 1.7 K or colder. A set of fountain-effect pumps sprays superfluid liquid helium onto each optical surface, producing helium flows of 50-100 cm3 s-1 at heights up to 200 cm above the liquid level. We describe the fountain-effect pumps and the cryogenic performance of the PIPER payload during two flights in 2017 and 2019.

Sub-Kelvin cooling for two kilopixel bolometer arrays in the PIPER receiver.

The Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne telescope mission to search for inflationary gravitational waves from the early universe. PIPER employs two 32 × 40 arrays of superconducting transition-edge sensors, which operate at 100 mK. An open bucket Dewar of liquid helium maintains the receiver and telescope optics at 1.7 K. We describe the thermal design of the receiver and sub-Kelvin cooling with a continuous adiabatic demagnetization refrigerator (CADR). The CADR operates between 70 and 130 mK and provides ≈10 µW cooling power at 100 mK, nearly five times the loading of the two detector assemblies. We describe electronics and software to robustly control the CADR, overall CADR performance in flightlike integrated receiver testing, and practical considerations for implementation in the balloon float environment.

On the redshift distribution and physical properties of ACT-selected DSFGs.

We present multi-wavelength detections of nine candidate gravitationally-lensed dusty star-forming galaxies (DSFGs) selected at 218GHz (1.4mm) from the ACT equatorial survey. Among the brightest ACT sources, these represent the subset of the total ACT sample lying in Herschel SPIRE fields, and all nine of the 218GHz detections were found to have bright Herschel counterparts. By fitting their spectral energy distributions (SEDs) with a modified blackbody model with power-law temperature distribution, we find the sample has a median redshift of z = 4.1 - 1.0 + 1.1 (68 per cent confidence interval), as expected for 218GHz selection, and an apparent total infrared luminosity of log 10 ( µ L IR / L ⊙ ) = 13.86 - 0.30 + 0.33 , which suggests that they are either strongly lensed sources or unresolved collections of unlensed DSFGs. The effective apparent diameter of the sample is µ d = 4.2 - 1.0 + 1.7 kpc , further evidence of strong lensing or multiplicity, since the typical diameter of dusty star-forming galaxies is 1.0-2.5 kpc. We emphasize that the effective apparent diameter derives from SED modelling without the assumption of optically thin dust (as opposed to image morphology). We find that the sources have substantial optical depth. ( τ = 4.2 - 1.9 + 3.7 ) to dust around the peak in the modified blackbody spectrum (λ obs ⩽ 500µm), a result that is robust to model choice.

A broadband micro-machined far-infrared absorber.

The experimental investigation of a broadband far-infrared meta-material absorber is described. The observed absorptance is >0.95 from 1 to 20 THz (300-15 µm) over a temperature range spanning 5-300 K. The meta-material, realized from an array of tapers ≈100 µm in length, is largely insensitive to the detailed geometry of these elements and is cryogenically compatible with silicon-based micro-machined technologies. The electromagnetic response is in general agreement with a physically motivated transmission line model.

Impedance matched absorptive thermal blocking filters.

We have designed, fabricated, and characterized absorptive thermal blocking filters for cryogenic microwave applications. The transmission line filter's input characteristic impedance is designed to match 50 Ω and its response has been validated from 0 to 50 GHz. The observed return loss in the 0 to 20 GHz design band is greater than 20 dB and shows graceful degradation with frequency. Design considerations and equations are provided that enable this approach to be scaled and modified for use in other applications.

A cryogenic infrared calibration target.

A compact cryogenic calibration target is presented that has a peak diffuse reflectance, R ⩽ 0.003, from 800 to 4800 cm(-1) (12 - 2 µm). Upon expanding the spectral range under consideration to 400-10,000 cm(-1) (25 - 1 µm) the observed performance gracefully degrades to R ⩽ 0.02 at the band edges. In the implementation described, a high-thermal-conductivity metallic substrate is textured with a pyramidal tiling and subsequently coated with a thin lossy dielectric coating that enables high absorption and thermal uniformity across the target. The resulting target assembly is lightweight, has a low-geometric profile, and has survived repeated thermal cycling from room temperature to ∼4 K. Basic design considerations, governing equations, and test data for realizing the structure described are provided. The optical properties of selected absorptive materials-Acktar Fractal Black, Aeroglaze Z306, and Stycast 2850 FT epoxy loaded with stainless steel powder-are characterized and presented.

Variable-delay polarization modulators for cryogenic millimeter-wave applications.

We describe the design, construction, and initial validation of the variable-delay polarization modulator (VPM) designed for the PIPER cosmic microwave background polarimeter. The VPM modulates between linear and circular polarization by introducing a variable phase delay between orthogonal linear polarizations. Each VPM has a diameter of 39 cm and is engineered to operate in a cryogenic environment (1.5 K). We describe the mechanical design and performance of the kinematic double-blade flexure and drive mechanism along with the construction of the high precision wire grid polarizers.

A waveguide-coupled thermally isolated radiometric source.

The design and validation of a dual polarization source for waveguide-coupled millimeter and sub-millimeter wave cryogenic sensors is presented. The thermal source is a waveguide mounted absorbing conical dielectric taper. The absorber is thermally isolated with a kinematic suspension that allows the guide to be heat sunk to the lowest bath temperature of the cryogenic system. This approach enables the thermal emission from the metallic waveguide walls to be subdominant to that from the source. The use of low thermal conductivity Kevlar threads for the kinematic mount effectively decouples the absorber from the sensor cold stage. Hence, the absorber can be heated to significantly higher temperatures than the sensor with negligible conductive loading. The kinematic suspension provides high mechanical repeatability and reliability with thermal cycling. A 33-50 GHz blackbody source demonstrates an emissivity of 0.999 over the full waveguide band where the dominant deviation from unity arises from the waveguide ohmic loss. The observed thermal time constant of the source is 40 s when the absorber temperature is 15 K. The specific heat of the lossy dielectric, MF-117, is well approximated by C(v)(T) = 0.12 T (2.06) mJ g(-1) K(-1) between 3.5 K and 15 K.