Session T26: Superconducting Qubits: Measurements

Non-degenerate parametric amplification with the Josephson ring modulator

We present recent progress in building and operating a new microwave design of the Josephson parametric converter (JPC). The JPC is a parametric microwave amplifier operating close to the quantum limit of noise. The device is based on two microwave resonators coupled to a Josephson ring modulator, which resembles a DC-SQUID but has four junctions instead of two and is biased with half a flux quantum. The non-linearity of the ring modulator is of the form XYZ and involves the minimal number of modes, placing the JPC close to the ideal non-degenerate parametric amplifier. Our new design allows fabrication in a single lithography step, greatly simplifying parameter adjustments from one device generation to the next. It further avoids awkward on-chip crossings between distinct microwave lines.   

Two-port directional parametric amplifier

Parametric amplifiers working at the quantum limit are indispensable for fast, accurate measurements of superconducting qubits and other sensitive mesoscopic systems. Conventional microwave parametric amplifiers usually operate as one-port reflection devices and rely on non-reciprocal components like circulators. Besides affecting the magnetic environment near delicate superconducting devices, circulators are problematic for on-chip integration owing to their relatively bulky size. We will present the results of a theoretical analysis of a minimal-noise directional amplifier based on parametric Josephson devices, which would avoid the need for circulators in quantum-limited measurements. The link between the non-reciprocal operation of this amplifier and the dynamics of the microwave dc SQUID amplifier will be discussed.   

Microwave oscillators based on dc SQUIDs

We have fabricated lumped-element microwave oscillators consisting of a dc SQUID with submicron Al-AlO$_{x}$-Al junctions shunted with a capacitor formed from superconducting layers. These circuits resonate in the range of several GHz. Adjusting the current through on-chip bias lines changes the Josephson inductance of the SQUID junctions, thus varying the resonance frequency. We discuss the prospects for time-domain monitoring of the ring-down oscillations following a bias current pulse in these circuits. The discrimination of ring-down signals for different flux bias forms the basis for employing these devices in a possible new readout scheme for superconducting flux qubits.   

Dispersive readout of a flux qubit using a microstrip SQUID amplifier

Dispersive techniques for the readout of superconducting qubits offer the possibility of high repetition-rate quantum non-demolition measurement by avoiding dissipation close to the qubit. We demonstrate a dispersive readout scheme in which a three junction aluminum flux qubit is inductively coupled to a 1-2 GHz oscillator formed by a capacitively shunted SQUID. The SQUID in this readout oscillator acts as a nonlinear, flux-dependent inductor so that the oscillator resonance frequency depends on the state of the qubit. Readout is performed by microwave reflectometry; the reflected signal is amplified using a microstrip SQUID amplifier (MSA) with a noise temperature of a few hundred millikelvin. This noise temperature is an order of magnitude lower than that of the HEMT (high electron mobility transistor) amplifier that follows the MSA. We report measurements in both the linear (weak drive) and the bistable (strong drive) oscillator regimes.   

Novel microwave readout for phase qubits

We present a novel microwave based readout for a phase qubit which circumvents loss mechanisms that have been shown to impact qubit coherence times. Additionally, this new technique facilitates multiplexing of qubits thereby reducing the number of cryogenic wires required for operating the qubits. The basic operation of the circuit will be discussed and compared with experimental data.   

Microstrip SQUID Amplifiers for Qubit Readout at Gigahertz Frequencies and Millikelvin Temperatures

The dispersive readout of superconducting flux qubits at very low excitation power is currently limited by the noise performance of cryogenic semiconductor HEMT amplifiers. To increase measurement sensitivity, we have fabricated and characterized low noise Microstrip SQUID Amplifiers (MSAs) operating in the 1.2 to 1.6 GHz frequency band. The MSA consists of a microstrip input coil, open at one end, inductively coupled to a SQUID washer which also serves as the microstrip ground plane. The input was critically coupled to a 50-$\Omega$ source via a capacitor to optimize the gain and bandwidth. At 25 mK we have observed stable forward gain up to 14 dB on resonance at 1.39 GHz with bandwidths of typically 20 MHz and noise temperatures of about 300 mK (Caves added noise number of about 4.0). This noise temperature is an order of magnitude lower than that of a typical HEMT. Higher frequency operation will be discussed.   

QND measurements of the Fluxonium artificial atom

We present Quantum Non-Demolition (QND) measurements of a Fluxonium qubit, which utilizes a Josephson junction array inductance to shunt the junction of a Cooper-pair box qubit. The Cooper-pair box is coupled capacitively to a readout cavity, which assesses the state of the qubit through a dispersive shift of the cavity frequency. By sending a microwave pulse at the cavity frequency and monitoring the phase of the reflected signal, a direct measurement of the qubit state is acquired after a preparation pulse. We will discuss the QND nature of the measurement, the use of sideband transitions for preparing the qubit state, and the prospect for single shot QND readout.   

Dispersive magnetometry with a noiseless SQUID parametric amplifier

We have realized a dispersive magnetometer circuit consisting of an unshunted dc SQUID in parallel with an on-chip capacitor. An input flux signal is encoded as a phase modulation of a microwave pump tone applied to this nonlinear resonator. This phase modulation creates a voltage signal in which all the information is contained in a single quadrature. For sufficiently strong microwave drive power, the nonlinearity of the resonator results in phase sensitive parametric amplification of the voltage signal with potentially zero added noise. We obtain an effective flux noise of $% 0.14$ $\mu \Phi _{0}\mathrm{Hz}^{-\frac{1}{2}}$ with 400 kHz bandwidth, corresponding to 32 dB of parametric gain at 5.56 GHz and an added noise of no greater than 0.14 photons. By reducing the parametric gain to 15 dB, we can increase the bandwidth to 20 MHz with an effective flux noise of $0.29$ $% \mu \Phi _{0}\mathrm{Hz}^{-\frac{1}{2}}.$ In these measurements, the SQUID never enters the voltage state. Thus, this technique is well suited to applications requiring low backaction, such as quantum state measurement. We acknowledge support from the AFOSR(RV, IS), the Hertz Foundation (DHS), and the DOE (MH, JC).   

Progress towards a broadband traveling wave Josephson parametric amplifier

Most Josephson parametric amplifiers are based on a resonant circuit architecture with associated bandwidth limitations. We examine the use of a `Josephson nonlinear fiber' -- a transmission line periodically loaded with Josephson junctions -- as an inherently broadband traveling wave parametric amplifier. We report on the device design, calculations of gain and bandwidth from a simple model, and preliminary measurement results. We acknowledge the ONR and the Hertz Foundation for financial support.   

Improved Microwave Amplifiers Based on the dc SQUID

The dc SQUID can be used as a sensitive microwave amplifier if the signal to be amplified is suitably coupled to the SQUID. We have designed and fabricated microwave amplifiers in which a coil integrated on top of the SQUID is operated as a half-wavelength-microstrip resonator. Such amplifiers have a power gain of up to 100 at 1 GHz, and 4 at 8 GHz. When cooled to millikelvin temperatures, sensitivities close to the quantum limited could be obtained at 500 MHz. By applying negative feedback and adding a few passive components, the input and output impedances of the amplifiers can be brought close to 50 ohms, with only a modest reduction in gain. The robust match to 50 ohms makes it possible to cascade multiple SQUID gain stages, and thereby enhance device performance. We describe novel configurations of the input resonator that allow operation at higher frequencies, and discuss application of these amplifiers to the readout of superconducting quantum circuits.   

Microstrip SQUID amplifiers with submicron junctions for enhanced gain

Recent progress in dc SQUID amplifiers suggests that these devices might approach quantum-limited sensitivity in the microwave range. With the signal coupled to the stripline resonance formed between the input coil and the SQUID washer -- the microstrip SQUID amplifier configuration -- gains of typically around 20 dB are possible at frequencies of several hundred MHz, and the gain is limited by the maximum voltage modulation available from the SQUID. Larger gain would be advantageous in pursuing the quantum limit and one route for achieving this involves using larger resistive shunts. However, maintaining nonhysteretic device operation requires smaller junction capacitances than is possible with conventional photolithographically patterned junctions. We have fabricated microstrip SQUID amplifiers using Al-AlO$_{x}$-Al submicron junctions and large shunts. These devices exhibit substantially larger gain than is possible with SQUIDs containing micron-sized junctions. We discuss the prospects for enhanced gain in the microwave range.   

Creating and Detecting a One Photon Fock State in Two Cavity CircuitQED

CircuitQED is an architecture which allows for strong interactions between single microwave photons and superconducting artificial atoms. This makes it an attractive testbed for the investigation of non-classical states of light. Previous work at Yale and elsewhere has shown the ability to detect the quantized field inside a superconducting coplanar waveguide cavity. In this talk I will show how this can be extended into a fast, QND detection scheme using an additional cavity and a quasi-dispersive interaction. This method is then used to monitor the decay of a single photon by repeated QND measurements.   

Tunable joint measurements in the dispersive regime of cavity QED

Joint measurements of multiple qubits have been shown to open new possibilities for quantum information processing. Here, we present an approach based on homodyne detection to realize such measurements in the dispersive regime of cavity QED. The readout can be tuned from extracting single-qubit to only multi-qubit properties like parity. We obtain a reduced stochastic master equation describing this measurement and its effect on the qubits. As an example, we present results for a parity measurement on two qubits that uses realistic parameters. In this situation, measurement of an initially unentangled state can yield a state of significant concurrence with probability approaching one.   

Anomalous switching curves in a dc SQUID phase qubit

We have measured switching curves (s-curves), Rabi oscillations (T'$\sim $160ns) and relaxation (T$_{1}\sim $280ns) in a dc SQUID phase qubit with an LC filter that provides good isolation from the bias leads at the operating frequency (3.5 GHz). The device is built on sapphire and has a 2 $\mu $m$^{2}$ Al/AlO$_{x}$/Al qubit junction shunted by a low-loss SiN$_{x}$ capacitor. To measure an s-curve, we apply microwaves to pump to a specific state and then find the probability that the device switches to the voltage state after a short ($\sim $2ns) current pulse is applied. As expected, the switching probability increases with the amplitude of the current pulse, is smallest in the ground state $\vert $0$>$ and largest in the excited state $\vert $1$>$. However, the s-curves for superposition states of $\vert $0$>$ and $\vert $1$>$ are anomalous - they are not the weighted sum of the $\vert $0$>$ and $\vert $1$>$ s-curves and the probability to switch is not linear in the excited state probability. Instead, the s-curves shift continuously along the current axis as the amplitude to be in $\vert $1$>$ increases. We will discuss the likely cause of this behavior and its implication for measurements in phase qubits.   

Dual-path measurements of propagating microwave signals at the quantum level for circuit QED

Few-photon propagating microwave signals can be characterized by means of a beam splitter and two amplification chains. We show that such a setup is robust against random noise added by the amplifiers. Even if this noise is much larger than the signal itself, the first two signal moments and, hence, Gaussian states can be analyzed via correlation measurements. We discuss possible applications of the dual-path method for detecting a squeezed state generated by a superconducting Josephson parametric amplifier and in circuit QED setups.