Physics

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Quantum coherent phenomena in superconducting circuits and ultracold atoms
(2010) Mitra, Kaushik; Lobb, Chris J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
This thesis consists of theoretical studies of superconducting qubits, and trapped bosons and fermions at ultracold temperature. In superconducting qubits I analyze the resonant properties and decoherence behavior of dc SQUID phase qubits, in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias lead. Typically qubit states in phase qubits are detected by tunneling it to the voltage state. I propose an alternate non-destructive readout mechanism which relies on the difference in the magnetic flux through the SQUID loop due to state of the qubit. I also study decoherence effects in a dc SQUID phase qubit caused by the isolation circuit. When the frequency of the qubit is at least two times larger than the resonance frequency of the isolation circuit, I find that the decoherence time of the qubit is two orders of magnitude larger than the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the isolation circuit. This theory is extended to other similar superconducting quantum devices and has been applied to experiments from the group at the University of Maryland. I also demonstrate, theoretically, vacuum Rabi oscillations, analogous to circuit-QED, in superconducting qubits coupled to an environment with resonance. The result obtained gives an exact analytical expression for coherent oscillation of state between the system (the qubit) and the environment with resonance. Next I investigate ultracold atoms in harmonically confined optical lattices. They exhibit a `wedding cake structure' of alternating Mott shells with different number of bosons per site. In regions between the Mott shells, a superfluid phase emerges at low temperatures which at higher temperatures becomes a normal Bose liquid. Using finite-temperature quantum field theoretic techniques, I find analytically the properties of the superfluid, Bose liquid, and Mott insulating regions. This includes the finite temperature order parameter equation for the superfluid phase, excitation spectrum, Berezinskii-Kosterlitz-Thouless transition temperature and vortex-antivortex pair formation (in the two dimensional case), finite temperature compressibility and density - density correlation function. I also study interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters I find emergence of superfluid and Fermi liquid (non-insulating) regions out of Bose-Mott and Fermi-band insulators, due to finite boson and fermion hopping. I also propose a possible experiment for the detection of superfluid and Fermi liquid shells through the use of Gauss-Laguerre and Gaussian beams followed by Bragg spectroscopy. Another area I explore is ultracold heteronuclear molecules such as KRb, RbCs and NaCs. I obtain the finite and zero-temperature phase diagram of bosons interacting via short range repulsive interactions and long-ranged isotropic dipolar interactions in two-dimensions. I build an analytical model for such systems that describes a first order quantum phase transition at zero temperature from a triangular crystalline phase (analogous to Wigner crystal phase of electrons) to superfluid phase. At finite temperature the crystalline phase melts, due to topological defects, to a hexatic phase where translational order is destroyed but hexagonal orientational order is preserved. Further temperature increase leads to the melting of the hexatic phase into a normal dipolar Bose liquid.
DISSIPATIVE AND DISPERSIVE MEASUREMENTS OF A COOPER PAIR BOX
(2010) Kim, Zaeill; Wellstood, Frederick C.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The quantum states of an Al/AlOx/Al Cooper pair box (CPB) qubit were measured at temperatures below 100 mK. Detailed spectroscopic measurements of the excited state of the CPB were made along with detailed measurements of the lifetime T1 of the first excited state. The CPB states were probed using radio-frequency (rf) techniques to read out using either an rf - single-electron transistor (rf-SET) or a low-loss superconducting resonator. Using an rf-SET, I measured the excited state spectrum of a CPB from 15 to 50 GHz. In this spectrum, a few anomalous avoided level crossings (ALC) were observed. These ALCs exhibited a strong gate voltage dependence and Josephson energy (Ej) dependence, consistent with a charge fluctuator coupled to the CPB island. A model Hamiltonian was used to fit the measured spectrum. Fitting parameters such as the charging energy Ec/h = 12.1 GHz and the Josephson energy Ej/h tuned between 2 GHz and 21 GHz for the CPB, and the well asymmetry, tunneling amplitude, and the minimum hopping distance for each fluctuator were extracted. The tunneling rates ranged from less than 3.5 to 13 GHz, i.e. values between 5 % and 150 % of the well asymmetry, and the dipole moments yield a minimum hopping distance of 0.3 to 0.8 Angstroms. I also made detailed measurements of the lifetime of the first excited state away from the CPB charge degeneracy point and found that the lifetime varied from less than 50 ns up to a few us as the Josephson energy Ej decreased, consistent with a charge noise (Sq~10-11 e2/Hz around 37 GHz to Sq~10-12 e2/Hz around 27 GHz) coupled to the qubit. I also found that at frequencies where an ALC was observed in the spectrum, a decrease in T1 occurred, suggesting that the discrete charge defects are a significant source of dissipation in the CPB. I also designed and fabricated a quasi-lumped element thin-film superconducting Al microwave resonator on sapphire to be used for a dispersive read-out of the CPB. The resonator consists of a meandering inductor and an interdigitated capacitor coupled to a transmission line. At T = 30 mK and on resonance at 5.578 GHz, the transmission through the transmission line decreased by 15 dB and the loaded quality factor was 60,000. I measured the temperature dependence of the resonator frequency and loss at temperatures as high as 500 mK and found reasonable agreement with the Mattis-Bardeen theory. Finally, I coupled a quasi-lumped element microwave resonator (f0~5.443 GHz), made of superconducting Al on sapphire, to an Al/AlOx/Al CPB qubit. Most of my measurements were made in the dispersive regime where Ej-hf0 is much larger than the coupling strength. In this case, the qubit causes a small state-dependent frequency shift in the resonator's resonant frequency. By sending down a second microwave tone (the pump), I was able to excite the CPB qubit. In zero magnetic field with the CPB far detuned from the resonator, I measured a 50 kHz decrease in f0 with the qubit in the ground state and biased near the degeneracy point of the CPB. The charging energy and Josephson energy of the CPB were determined from spectroscopy taken by saturating the CPB with a second microwave tone and measuring the transmission through the resonator. The first device had Ec/h = 12.5 GHz and maximum Ej/h = 9 GHz. The second device had Ec/h = 6.24 GHz and Ej/h tuned between 4 GHz and 8 GHz. By changing the external magnetic field, I could decrease the effective Ej of the CPB. From modeling, I extracted coupling strengths g/2&pi = 11 MHz and 5 MHz for the first and second device, respectively. Finally I did single and two-tone spectroscopy, and measured the relaxation and Rabi oscillations of the CPB. From the first device, I was able to obtain relaxation times T1 of 10.3 us at Ej/h = 7 GHz on the CPB degeneracy point and spectroscopic coherence times T2 *~ 100 ns. From the second device, I found relaxation times T1 of 200 us at Ej/h = 4 GHz to 4.5 GHz decreasing down to 4 us around 8 GHz. There was also a depression in T1 around the resonant frequency of the resonator. The Rabi decay times were found to be up to T'~ 330 ns.
Multi-Valley Physics of Two-Dimensional Electron Systemson Hydrogen-Terminated Silicon (111) Surfaces
(2010) McFarland, Robert Nicholas; Kane, Bruce E; Drew, Howard D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Recent work on two dimensional electron systems (2DES) has focused increasingly on understanding the way the presence of additional degrees of freedom (e.g. spin, valleys, subbands, and multiple charge layers) affect transport as such effects may be critical to the development of nanoscale and quantum devices and may lead to the discovery of new physics . In particular, conduction band valley degeneracy opens up a rich parameter space for observing and controlling 2DES behavior. Among such systems, electrons on the (111) surface of silicon are especially notable because effective mass theory predicts the conduction band to be sixfold degenerate, for a total degeneracy (spin ×valley) of 12 in the absence of a magnetic field B. Previous investigations of Si(111) transport using Metal-Oxide-Semiconductor Field Effect Transistors (MOSFETs) observed a valley degeneracy g_v of 2 except in certain specially prepared samples with low mobility. We have developed a novel device architecture for investigating transport on a H-Si(111)-vacuum interface free from the complications created by intrinsic disorder at Si-SiO₂ interfaces. The resulting devices display very high mobilities (up to 110,000 cm2/Vs at 70 mK, more than twice as large as the best silicon MOSFETs), enabling us to probe valley-dependent transport to a much greater degree than previously possible. In particular, we observed detailed Integer Quantum Hall structure with hints of Fractional states as well. These devices display clear evidence of six occupied valleys, including strongly “metallic” temperature dependence expected for large g_v. Some devices show strong sixfold degeneracy while others display a partial lifting of the degeneracy, resulting in unequal distribution of electrons among the six valleys. This symmetry breaking results in anisotropic transport at low B fields, but other observed anisotropies remain unexplained. Finally, we apply this unusual valley structure to show how corrections to the low-B magnetoresistance and Hall effect can provide information about valley-valley interactions. We propose a model of valley drag, similar to Coulomb drag in bilayer systems, and find good agreement with our experimental data, though a small residual drag in the T→0 limit remains unexplained.
LINK BETWEEN DYNAMICS AND FUNCTION IN SINGLE AND MULTI-SUBUNIT ENZYMES
(2010) Chen, Jie; Thirumalai, Devarajan; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Biopolymers, such as proteins and DNA, are polymers whose three-dimensional conformations dene their biological functions. Current emphasis on structures has greatly advanced our understanding of the functions of biopolymers. However, there is a need to understand the deeper link between biopolymer dynamics and function, because in water and under cellular conditions, everything that biopolymers do can be understood in terms of "the jigglings and wigglings of atoms". These motions arise from thermal noise in the solvent and due to intrinsic motion of the enzymes. In biological systems, the motions are often highly regulated to ensure that cellular processes are executed over the required time scales. For enzymes, which are essentially proteins that catalyze chemical reactions or generate mechanical work, conformational fuctuations are coupled at various stages through interactions with ligands during the catalytic cycle. We have studied two dierent enzymes, dihydrofolate reductase (DHFR), which catalyzes reduction of dihydrofolate to tetrahydrofolate, and RNA polymerase (RNAP from bacteria and Pol II from yeast), which is responsible for RNA synthesis using DNA as a template. In order to study the link between dynamics and function we have developed new methods and extended a variety of computational techniques. For DHFR, we use both evolutionary imprints (SCA) and structure-based perturbation method (SPM) to extract a network of residues that facilitate the transitions between two distinct conformational states (closed and occluded states). The transition kinetics and pathways connecting the closed and occluded states are described using Brownian dynamics (BD) simulation. We found the sliding motion of Met20 loop across helix 2 is involved in the forward and reverse transitions between the closed and occluded states. We also found that cross-linking M16-G121 inhibits both the forward and the reverse transitions. In addition, we showed the transition states of these transitions are broad and resemble high energy states. For RNAP, we focus on the conformational changes of RNAP and DNA in promoter melting process. Using BD, we show that DNA conformation changes in promoter melting occur in three steps. We also show that internal dynamics of RNAP is relevant to facilitate the bending of DNA. For Pol II, the structural transitions between two initiation conformational states and between initiation state and elongation state are studied using SPM and BD. We determine the structural units that regulate structural transitions and describe the transition kinetics. The combination of three dierent methods, SCA, SPM and BD, provide results that are in accord with many experiments. Moreover, our description of the detailed structural transitions in these enzymes lead to new insights and testable predictions in these extraordinarily important enzyme functions.
Experimental Characterization of Turbulent Superfluid Helium
(2010) Paoletti, Matthew S.; Lathrop, Daniel P; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Fundamental processes in turbulent superfluid 4He are experimentally characterized by refining a visualization technique recently introduced by Bewley et al. A mixture of hydrogen and helium gas is injected into the bulk fluid, which produces a distribution of micron-sized hydrogen tracer particles that are visualized and individually tracked allowing for local velocity measurements. Tracer trajectories are complex since some become trapped on the quantized vortices while others flow with the normal fluid. This technique is first applied to study the dynamics of a thermal counterflow. The resulting observations constitute the first direct confirmation of two-fluid motions in He II and provide a quantitative test of the expression for the dependence of the normal fluid velocity, v_n, on the applied heat flux, q, derived by L. D. Landau in 1941. Nearly 20,000 individual reconnection events are identified for the first time and used to characterize the dynamics by the minimum separation distance, $delta(t)$, between two reconnecting vortices. Dimensional arguments predict that this separation behaves asymptotically as $delta(t) approx A left ( kappa vert t-t_0 vert right ) ^{1/2}$, where $kappa=h/m$ is the quantum of circulation. The major finding of the experiments is strong support for this asymptotic form with $kappa$ as the dominant controlling quantity. Nevertheless there are significant event-to-event fluctuations that are equally well fit by two modified expressions: (a) an arbitrary power-law expression $delta(t)=B vert t-t_0 vert ^{alpha}$ and (b) a correction-factor expression $delta(t)=Aleft (kappa vert t-t_0 vert right ) ^{1/2}(1+c vert t-t_0 vert )$. In light of various physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and boundary conditions, as best describing the experimental data. The observed dynamics appear statistically time-reversible, suggesting that an effective equilibrium has been established in quantum turbulence on the time scales investigated. The hydrogen tracers allow for the first measurements of the local velocity statistics of a turbulent quantum fluid. The distributions of velocity in the decaying turbulence are strongly non-Gaussian with 1/v3 power-law tails in contrast to the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. The dynamics of many vortex reconnection events are examined and simple scaling arguments show that they yield the observed power-law tails.
Characterization of Quantum Efficiency and Robustness of Cesium-Based Photocathodes
(2010) Montgomery, Eric J.; O'Shea, Patrick G.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
High quantum efficiency, robust photocathodes produce picosecond-pulsed, high-current electron beams for photoinjection applications like free electron lasers. In photoinjectors, a pulsed drive laser incident on the photocathode causes photoemission of short, dense bunches of electrons, which are then accelerated into a relativistic, high quality beam. Future free electron lasers demand reliable photocathodes with long-lived quantum efficiency at suitable drive laser wavelengths to maintain high current density. But faced with contamination, heating, and ion back-bombardment, the highest efficiency photocathodes find their delicate cesium-based coatings inexorably lost. In answer, the work herein presents careful, focused studies on cesium-based photocathodes, particularly motivated by the cesium dispenser photocathode. This is a novel device comprised of an efficiently photoemissive, cesium-based coating deposited onto a porous sintered tungsten substrate, beneath which is a reservoir of elemental cesium. Under controlled heating cesium diffuses from the reservoir through the porous substrate and across the surface to replace cesium lost to harsh conditions -- recently shown to significantly extend the lifetime of cesium-coated metal cathodes. This work first reports experiments on coated metals to validate and refine an advanced theory of photoemission already finding application in beam simulation codes. Second, it describes a new theory of photoemission from much higher quantum efficiency cesium-based semiconductors and verifies its predictions with independent experiment. Third, it investigates causes of cesium loss from both coated metal and semiconductor photocathodes and reports remarkable rejuvenation of full quantum efficiency for contaminated cesium-coated surfaces, affirming the dispenser prescription of cesium resupply. And fourth, it details continued advances in cesium dispenser design with much-improved operating characteristics: lower temperature and cleaner operation. Motivated by dispenser integration with semiconductor coatings, initial fabrication of those coatings are reported on dispenser-type substrates with measurement of quantum efficiency and analysis of thermal stability. Detailed investigations are performed on dispenser substrate preparation by ion beam cleaning and on dispenser pore structure by electron microscopy and focused ion beam milling. The dissertation concludes by discussing implications of all results for the demonstration and optimization of the future high quantum efficiency cesium dispenser photocathode.
EXPLORATION OF NOVEL METHODS FOR THE FABRICATION AND CHARACTERIZATION OF ORGANIC FIELD-EFFECT TRANSISTORS AND EXAMINATION OF FACTORS INFLUENCING OFET PERFORMANCE
(2009) Southard, Adrian Edward; Fuhrer, Michael S.; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
This thesis explores novel methods for fabricating organic field effect transistors (OFETs) and characterizing OFET devices. Transfer printing is a promising process for fabricating organic thin-film devices. In this work, a transfer-printing process is developed for the polymer organic semiconductor P3HT. Pre-patterned P3HT is printed onto different dielectrics such as PMMA, polystyrene and polycarbonate. The P3HT layer is spun on a smooth silicon interface made hydrophobic by treatment with octyltrichlorosilane, which functions as a release layer. This method has distinct advantages over standard OFET fabrication methods in that 1) the active layer can be pre-patterned, 2) the solvent for the P3HT need not be compatible with the target substrate, and 3) the electrical contact formed mimics the properties of top contacts but with the spatial resolution of bottom contacts. Transparent, conducting films of carbon nanotubes (CNTs) are prepared by airbrushing, and characterized optically and electronically. OFETs with CNT films as source and drain electrodes are fabricated using various patterning techniques, and the organic/CNT contact resistance is characterized. CNT films make transparent, flexible electrodes with contact resistance comparable to that found for Au bottom-contacted P3HT transistors and comparable to CNT-film bottom-contacted pentacene transistors with CNTs deposited by other less flexible methods. A transparent OFET is demonstrated using transfer printing for the assembly of an organic semiconductor (pentacene), CNT film source, drain, and gate electrodes, and polymer gate dielectric and substrate. The dependence of the conductance and mobility in pentacene OFETs on temperature, gate voltage, and source-drain electric field is studied. The data are analyzed by extending a multiple trapping and release model to account for lowering of the energy required to excite carriers into the valence band (Poole-Frenkel effect). The temperature-dependent conductivity shows activated behavior, and the activation energy is lowered roughly linearly with the square-root of electric field, as expected for the Poole-Frenkel effect. The gate voltage dependence of the activation energy is used to extract the trap density of states, in good agreement with other measurements in the literature.
STEPS ON VICINAL SURFACES: DENSITY-FUNCTIONAL THEORY CALCULATIONS AND TRANSCENDING MINIMAL STATISTICAL-MECHANICAL MODELS
(2009) Sathiyanarayanan, Rajesh; Einstein, Theodore L; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Using both density-functional theory calculations and Monte Carlo simulations, we compute various key parameters that are used to model steps on vicinal surfaces. In the first part, we discuss the importance of multi-site interactions (trios and quartos) in the lattice-gas characterization of adatom interactions. Using density-functional theory calculations, we show that multi-site interactions with substantial contributions from direct interactions are sensitive to adatom relaxations. Such sensitivity to adatom relaxations complicates the lattice-gas approach to modeling overlayer systems. Our results show that a careful consideration of relaxation effects is required to make connections with experiments. In the second part, we use both density-functional theory calculations and kinetic Monte Carlo simulations to identify the impurity atom responsible for growth instabilities on Cu vicinals. In addition to that, we also show that a small quantity of codeposited impurities significantly alters the growth behavior. Our results indicate that growth morphologies could be controlled through the codeposition of an appropriate impurity. Hence, impurities could play a crucial role in nanostructuring of surfaces. Step configurations have fruitfully been related to the worldlines of spinless fermions in one dimension. However, in addition to the realistic no-crossing condition, the fermion picture imposes a more restrictive non-touching condition. in the third part of this thesis, we use Metropolis Monte Carlo method to study the effects of loosening this non-touching condition on the resulting TWDs. Our results show that allowing step touching leads to an effective attraction in the step-step interaction strength measurements. We show that this effective attraction can be incorporated into the fermion picture as a finite-size effect.
CARBON NANOTUBE THIN FILM AS AN ELECTRONIC MATERIAL
(2009) Sangwan, Vinod Kumar; Williams, Ellen D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Carbon nanotubes (CNT) are potential candidates for next-generation nanoelectronics devices. An individual CNT possesses excellent electrical properties, but it has been extremely challenging to integrate them on a large-scale. Alternatively, CNT thin films have shown great potential as electronic materials in low cost, large area transparent and flexible electronics. The primary focus of this dissertation is patterning, assembling, characterization and assessment of CNT thin films as electronic material. Since a CNT thin film contains both metallic and semiconducting CNTs, it can be used as an active layer as well as an electrode material by controlling the growth density and device geometry. The growth density is controlled by chemical vapor deposition and airbrushing methods. The device geometry is controlled by employing a transfer printing method to assemble CNT thin film transistors (TFT) on plastic substrates. Electrical transport properties of CNT TFTs are characterized by their conductance, transconductance and on/off ratio. Optimized device performance of CNT TFTs is realized by controlling percolation effects in a random network. Transport properties of CNTs are affected by the local environment. To study the intrinsic properties of CNTs, the environmental effects, such as those due to contact with the dielectric layer and processing chemicals, need to be eliminated. A facile fabrication method is used to mass produce as-grown suspended CNTs to study the transport properties of CNTs with minimal effects from the local environment. Transport and low-frequency noise measurements are conducted to probe the intrinsic properties of CNTs. Lastly, the unique contrast mechanism of the photoelectron emission microscopy (PEEM) is used to characterize the electric field effects in a CNT field effect transistor (FET). The voltage contrast mechanism in PEEM is first characterized by comparing measurements with simulations of a model system. Then the voltage contrast is used to probe the local field effects on a single CNT and a CNT thin film. This real-time imaging method is assessed for potential applications in testing of micron sized devices integrated in large scale.
Back-Action Evading Measurements of Nanomechanical Motion Approaching Quantum Limits
(2009) Hertzberg, Jared Barney; Schwab, Keith C; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 1010 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 106. By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.

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