arXiv subjects

A. J. Rimberg

Publications and source records attributed to A. J. Rimberg.

At least 19 recordsLinked to original sources

arXiv2022

Feedback stabilization of the resonant frequency in tunable microwave cavities with single-photon occupancy

We successfully demonstrate low-frequency noise suppression in the resonant frequency fluctuations of a cavity-embedded Cooper pair transistor (cCPT) driven at single-photon occupancy. In particular, we report a reduction in the resonant frequency fluctuations caused by the internal charge noise over a bandwidth of $\sim$1.4 kHz when the cavity is driven at an average photon number $n=10$, and a bandwidth of 11 Hz for average $n=1$. The gate-dependent tunability of the cCPT allows us to implement a feedback-scheme, derived from the Pound-Drever-Hall locking technique. This reduces fluctuations due to intrinsic charge-noise, which otherwise interferes with the cCPT's operation as a near quantum-limited electrometer. We believe our technique can be generalized to achieve frequency stabilization in tunable microwave resonators that play a vital role in today's quantum computing architecture, thereby moderating the limitations in detection caused by the intrinsic $1/f$-noise on such circuit devices. The work discusses the various aspects relating to the operation of a fully functional feedback loop down to the single-photon level.

quant-ph↗

arXiv2021

Fast and Ultrasensitive Electrometer Operating at the Single-Photon Level

We demonstrate fast and ultrasensitive charge detection with a cavity-embedded Cooper pair transistor (cCPT) via dispersive readout of its Josephson inductance. We report a minimum charge sensitivity of $14$ $μe/\sqrt{\mathrm{Hz}}$ with a detection bandwidth on the order of $1$ MHz using $16$ attowatts of power, corresponding to the single-photon level of the cavity. In addition, our measured sensitivities are within a factor of $5$ of the quantum limit for this device. The single-photon-level sensitivity of the cCPT is comparable to that of the rf-SET, which typically operates using picowatts of power corresponding to hundreds of thousands of photons in its tank circuit. Our results support the feasibility of using the cCPT to mediate an optomechanical interaction that reaches the single-photon strong coupling regime.

cond-mat.mes-hall↗

arXiv2021

Charge sensitivity of a cavity-embedded Cooper pair transistor limited by single-photon shot noise

Using an operator scattering approach, we analyze the quantum dynamics of an ultrasensitive electrometer -- a Cooper pair transistor embedded in a quarter-wave microwave cavity (cCPT). While the cCPT is inherently a tunable, strongly nonlinear system affording a diverse range of functionalities, we restrict our present analysis to a necessary first investigation of its linear charge sensing capabilities, limiting to low pump powers corresponding to an average cavity photon number $\lesssim 1$. Assuming realizable cCPT parameters (B. L. Brock et al., Phys. Rev. Applied, 044009), and not including noise from the subsequent amplifier chain, we predict the fundamental, photon shot noise-limited charge sensitivity to be $0.12\, μ{\mathrm{e}}/\sqrt{\mathrm{Hz}}$ when the pumped cavity has an average of one photon and the cCPT is operated close to charge degeneracy. This is to be compared with a first reported charge sensitivity value $14\, μ{\mathrm{e}}/\sqrt{\mathrm{Hz}}$ in the single-photon regime (B. L. Brock et al., arXiv:2102.05362).

cond-mat.mes-hall↗

arXiv2021

A Nonlinear Charge- and Flux-Tunable Cavity Derived from an Embedded Cooper Pair Transistor

We introduce the cavity-embedded Cooper pair transistor (cCPT), a device which behaves as a highly nonlinear microwave cavity whose resonant frequency can be tuned both by charging a gate capacitor and by threading flux through a SQUID loop. We characterize this device and find excellent agreement between theory and experiment. A key difficulty in this characterization is the presence of frequency fluctuations comparable in scale to the cavity linewidth, which deform our measured resonance circles in accordance with recent theoretical predictions [Brock et al., Phys. Rev. Applied 14, 054026 (2020)]. By measuring the power spectral density of these frequency fluctuations at carefully chosen points in parameter space, we find that they are primarily a result of the $1/f$ charge and flux noise common in solid state devices. Notably, we also observe key signatures of frequency fluctuations induced by quantum fluctuations in the cavity field via the Kerr nonlinearity.

cond-mat.mes-hall↗

arXiv2020

Frequency Fluctuations in Tunable and Nonlinear Microwave Cavities

We present a model for how frequency fluctuations comparable to the total cavity linewidth may arise in tunable and nonlinear microwave cavities, and how these fluctuations affect the measurement of scattering matrix elements. Applying this model to the specific case of a two-sided cavity, we obtain closed-form expressions for the average scattering matrix elements in several important cases. A key signature of our model is the subtle deformation of the trajectories swept out by scattering matrix elements in the complex plane. Despite this signature, the fluctuating and non-fluctuating models are qualitatively similar enough to be mistaken for one another. In the case of tunable cavities we show that if one fails to account for these fluctuations then one will find damping rates that appear to depend on the tuning parameter, which is a common observation in such systems. In the case of a Kerr cavity, we show that there exists a fundamental lower bound to the scale of these frequency fluctuations in the steady state, imposed by quantum mechanical uncertainty, which can appreciably affect the apparent damping rates of the cavity as the strength of the nonlinearity approaches the single-photon level. By using the model we present as a fitting function for experimental data, however, one can extract both the true damping rates of the cavity and the effective scale of these frequency fluctuations over the scattering measurement's bandwidth. Lastly, we compare this new method for observing frequency fluctuations to other methods, one of which we extend beyond the regime of small fluctuations.

cond-mat.mes-hall↗

arXiv2018

Mechanically Generating Entangled Photons from the Vacuum: A Microwave Circuit-Acoustic Resonator Analogue of the Unruh Effect

We consider a model for an oscillatory, relativistic accelerating photodetector inside a cavity and show that the entangled photon pair production from the vacuum (Unruh effect) can be accurately described in the steady state by a non-degenerate parametric amplifier (NDPA), with the detector's accelerating center of mass serving as the parametric drive (pump). We propose an Unruh effect analogue NDPA microwave superconducting circuit scheme, where the breathing mode of the coupling capacitance between the cavity and detector provides the mechanical pump. For realizable circuit parameters, the resulting photon production from the vacuum should be detectable.

quant-ph↗

arXiv2017

Quantum Dynamics of a Josephson Junction-Driven Cavity Mode System in the Presence of Voltage Bias Noise

We give a semiclassical analysis of the average photon number as well as photon number variance (Fano factor $F$) for a Josephson-junction (JJ) embedded microwave cavity system, where the JJ is subject to a fluctuating (i.e. noisy) bias voltage with finite dc average. Through the ac Josephson effect, the dc voltage bias drives the effectively nonlinear microwave cavity mode into an amplitude squeezed state ($F<1$), as has been established previously [A. D. Armour, et al., Phys. Rev. Lett. 111, 247001 (2013)], but bias noise acts to degrade this squeezing. We find that the sensitivity of the Fano factor to bias voltage noise depends qualitatively on which stable fixed point regime the system is in for the corresponding classical nonlinear steady state dynamics. Furthermore, we show that the impact of voltage bias noise is most significant when the cavity is excited to states with large average photon number.

cond-mat.mes-hall↗

arXiv2014

Iterative solutions to the steady state density matrix for optomechanical systems

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.

quant-ph↗

arXiv2014

Signatures of Valley Kondo Effect in Si/SiGe Quantum Dots

We report measurements consistent with the valley Kondo effect in Si/SiGe quantum dots, evidenced by peaks in the conductance versus source-drain voltage that show strong temperature dependence. The Kondo peaks show unusual behavior in a magnetic field that we interpret as arising from the valley degree of freedom. The interplay of valley and Zeeman splittings is suggested by the presence of side peaks, revealing a zero-field valley splitting between 0.28 to 0.34 meV. A zero-bias conductance peak for non-zero magnetic field, a phenomenon consistent with valley non- conservation in tunneling, is observed in two samples.

cond-mat.mes-hall↗

arXiv2013

A cavity-Cooper pair transistor scheme for investigating quantum optomechanics in the ultra-strong coupling regime

We propose a scheme involving a Cooper pair transistor (CPT) embedded in a superconducting microwave cavity, where the CPT serves as a charge tunable quantum inductor to facilitate ultra-strong coupling between photons in the cavity and a nano- to meso-scale mechanical resonator. The mechanical resonator is capacitively coupled to the CPT, such that mechanical displacements of the resonator cause a shift in the CPT inductance and hence the cavity's resonant frequency. The amplification provided by the CPT is sufficient for the zero point motion of the mechanical resonator alone to cause a significant change in the cavity resonance. Conversely, a single photon in the cavity causes a shift in the mechanical resonator position on the order of its zero point motion. As a result, the cavity-Cooper pair transistor (cCPT) coupled to a mechanical resonator will be able to access a regime in which single photons can affect single phonons and vice versa. Realizing this ultra-strong coupling regime will facilitate the creation of non-classical states of the mechanical resonator, as well as the means to accurately characterize such states by measuring the cavity photon field.

cond-mat.mes-hall↗

arXiv2013

A Single-Cooper-Pair Josephson Laser

The advent of quantum optical techniques based on superconducting circuits has opened new regimes in the study of the non-linear interaction of light with matter. Of particular interest has been the creation of non-classical states of light, which are essential for continuous-variable quantum information processing, and could enable quantum-enhanced measurement sensitivity. Here we demonstrate a device consisting of a superconducting artificial atom, the Cooper pair transistor, embedded in a superconducting microwave cavity that may offer a path toward simple, continual production of non-classical photons. By applying a dc voltage to the atom, we use the ac Josephson effect to inject photons into the cavity. The backaction of the photons on single-Cooper-pair tunneling events results in a new regime of simultaneous quantum coherent transport of Cooper pairs and microwave photons. This single-pair Josephson laser offers great potential for the production of amplitude-squeezed photon states and a rich environment for the study of the quantum dynamics of nonlinear systems.

cond-mat.supr-con↗

arXiv2013

Universal quantum fluctuations of a cavity mode driven by a Josephson junction

We analyze the quantum dynamics of a superconducting cavity coupled to a voltage biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.

cond-mat.mes-hall↗

arXiv2011

Pauli spin blockade and lifetime-enhanced transport in a Si/SiGe double quantum dot

We analyze electron transport data through a Si/SiGe double quantum dot in terms of spin blockade and lifetime-enhanced transport (LET), which is transport through excited states that is enabled by long spin relaxation times. We present a series of low-bias voltage measurements showing the sudden appearance of a strong tail of current that we argue is an unambiguous signature of LET appearing when the bias voltage becomes greater than the singlet-triplet splitting for the (2,0) electron state. We present eight independent data sets, four in the forward bias (spin-blockade) regime and four in the reverse bias (lifetime-enhanced transport) regime, and show that all eight data sets can be fit to one consistent set of parameters. We also perform a detailed analysis of the reverse bias (LET) regime, using transport rate equations that include both singlet and triplet transport channels. The model also includes the energy dependent tunneling of electrons across the quantum barriers, and resonant and inelastic tunneling effects. In this way, we obtain excellent fits to the experimental data, and we obtain quantitative estimates for the tunneling rates and transport currents throughout the reverse bias regime. We provide a physical understanding of the different blockade regimes and present detailed predictions for the conditions under which LET may be observed.

cond-mat.mes-hall↗

arXiv2011

Si/SiGe quantum dot with superconducting single-electron transistor charge sensor

We report a robust process for fabrication of surface-gated Si/SiGe quantum dots (QDs) with an integrated superconducting single-electron transistor (S-SET) charge sensor. A combination of a deep mesa etch and AlOx backfill is used to reduce gate leakage. After the leakage current is suppressed, Coulomb oscillations of the QD and the current-voltage characteristics of the S-SET are observed at a temperature of 0.3 K. Coupling of the S-SET to the QD is confirmed by using the S-SET to perform sensing of the QD charge state.

cond-mat.mes-hall↗

arXiv2011

Introduction of a DC Bias into a High-Q Superconducting Microwave Cavity

We report a technique for applying a dc voltage or current bias to the center conductor of a high-quality factor superconducting microwave cavity without significantly disturbing selected cavity modes. This is accomplished by incorporating dc bias lines into the cavity at specific locations. The measured S-matrix parameters of the system are in good agreement with theoretical predictions and simulations. We find that at 4 K the quality factor of the cavity degrades by less than 1% under the application of a dc bias.

cond-mat.supr-con↗

arXiv2009

Analogue Hawking Radiation in a dc-SQUID Array Transmission Line

We propose the use of a superconducting waveguide formed from an array of dc-SQUID's for investigating analogue Hawking radiation. Biasing the array with a space-time varying flux modifies the propagation velocity of the waveguide, leading to an effective metric with an horizon. Being a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as back-reaction and analogue space-time fluctuations on the Hawking process.

quant-ph↗

arXiv2008

Spin blockade and lifetime-enhanced transport in a few-electron Si/SiGe double quantum dot

Spin blockade occurs when an electron is unable to access an energetically favorable path through a quantum dot due to spin conservation, resulting in a blockade of the current through the dot. Spin blockade is the basis of a number of recent advances in spintronics, including the measurement and the manipulation of individual electron spins. We report measurements of the spin blockade regime in a silicon double quantum dot, revealing a complementary phenomenon: lifetime-enhanced transport. We argue that our observations arise because the decay times for electron spins in silicon are long, enabling the electron to maintain its spin throughout its transit across the quantum dot and access fast paths that exist in some spin channels but not in others. Such long spin lifetimes are important for applications such as quantum computation and, more generally, spintronics.

cond-mat.mes-hall↗

arXiv2008

Quantum Noise, Effective Temperature, and Damping in a Superconducting Single-Electron Transistor

We have directly measured the quantum noise of a superconducting single-electron transistor (S-SET) embedded in a microwave resonator consisting of a superconducting LC tank circuit. Using an effective bath description, we find that the S-SET provides damping of the resonator modes proportional to its differential conductance and has an effective temperature that depends strongly on the S-SET bias conditions. In the vicinity of a double Cooper pair resonance, when both resonances are red detuned the S-SET effective temperature can be well below both the ambient temperature and the energy scale of the bias voltage. When blue detuned, the S-SET shows negative differential conductivity,

cond-mat.mes-hall↗