Dc SQUID Phase Qubit Research Articles

DC SQUID Phase Qubit Coupled to an On-Chip LC Resonator

We have fabricated and tested an Al/AlOx/Al dc SQUID phase qubit on a sapphire substrate with a qubit junction area 0.17 μm2 and critical current I0,J1 = 1.4 μA. The qubit is shunted by an interdigitated capacitor and isolated from the bias leads by an inductive isolation network using a larger Josephson junction with area 2 μm2 and critical current I0,J2 = 29 μA. Additional high-frequency filtering is provided by an on-chip LC filter, which consists of square spiral inductors and parallel plate SiNx capacitors. From detuned Rabi oscillation measurements, we estimate a relaxation time T1 ≈ 400 ns and dephasing time TΦ 1700 ns. Additionally, we observe that the qubit transition spectrum has multiple equally spaced subpeaks. These subpeaks are caused by coupling between the phase qubit and the LC filter, forming a Jaynes-Cummings system. Each individual subpeak corresponds to transitions with different photon numbers in the LC filter.

Coherent Frequency Conversion in a Superconducting Artificial Atom with Two Internal Degrees of Freedom

By adding a large inductance in a dc-SQUID phase qubit loop, one decouples the junctions' dynamics and creates a superconducting artificial atom with two internal degrees of freedom. In addition to the usual symmetric plasma mode (s mode) which gives rise to the phase qubit, an antisymmetric mode (a mode) appears. These two modes can be described by two anharmonic oscillators with eigenstates |ns> and |na> for the s and a mode, respectively. We show that a strong nonlinear coupling between the modes leads to a large energy splitting between states |0s,1a> and |2s,0a>. Finally, coherent frequency conversion is observed via free oscillations between the states |0s,1a> and |2s,0a>.

Anomalous Switching Curves in a dc SQUID Phase Qubit

We have observed anomalous switching curves (s-curves) in a dc SQUID phase qubit. The SQUID has two Al/AlOx/Al Josephson junctions in a 1.5 nH loop. One junction as a phase qubit and the other acts as a detector junction. The qubit junction area is 2 μm2, the critical current is 0.08 μA and the junction has an added low-loss SiNx shunting capacitor. The 1.37 μA detector junction is isolated from the bias leads by an on-chip inductor-capacitor (LC) network with a 130 MHz cut-off. We measure the state of the system at 20 mK by sending a short current pulse to the device and monitoring whether it switches to the voltage state. The s-curves for the ground state (0) and excited state (1) look much as expected. However, unlike previous results on phase qubits, when the device is pumped to a superposition state, the resulting s-curve is not a weighted sum of the s-curves for the 0 and 1 state. Instead, the s-curve appears to shift to lower pulse current with increasing amplitude to be in the 1 state. We examine this behavior and discuss implications for measurement of quantum superposition states in this system.

Identifying Sources of Decoherence in a dc SQUID Phase Qubit With a Sub-$\mu{\rm m}$ Junction and Interdigitated Capacitor

We fabricated a dc SQUID phase qubit with a sub- μm Al/AlOx/Al qubit junction and an interdigitated shunting capacitor on a sapphire substrate. The qubit junction had a critical current of 135 nA, and the isolation junction had a critical current of 8.3 μA. The shunting capacitance was about 1.5 pF. To reduce the unwanted effects of two-level systems and increase the relaxation time T1, we have removed unnecessary dielectrics, used a small qubit junction area (450 nm × 500 nm), isolated the qubit from the leads with an on-chip LC filter, and fabricated the device on a bare sapphire substrate. However, at a temperature of 20 mK, we found T1 ≈ 300 ns and the coherence time T2 ≈ 110 ns, which was much lower than one would expect from loss attributed to the leads and to dielectrics in the tunnel junction and substrate. Measurements of T1 versus applied flux (which tuned the qubit frequency) revealed a correlation between the strength of the coupling of the microwave excitation line to the qubit and the rate of energy dissipation in the qubit. This result suggests that the relaxation time was being limited by coupling to the microwave line.

Multilevel spectroscopy of two-level systems coupled to a dc SQUID phase qubit

We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc SQUID phase qubit with a 16 \mu\m2 area Al/AlOx/Al junction. Applying microwaves in the 10 GHz to 11 GHz range, we found eight avoided level crossings with splitting sizes from 10 MHz to 200 MHz and spectroscopic lifetimes from 4 ns to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with non-interacting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20-22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.

Dc SQUID Phase Qubit With an LC Filter

We describe the design of an inductor-capacitor (LC) network to increase the isolation of a dc SQUID phase qubit from its current bias leads and thereby increase the relaxation time T1 and coherence time T2. One junction in the SQUID acts as an ideal phase qubit while the second junction and the SQUID loop inductance act as a broadband inductive filter to isolate the first junction from the current bias leads. The LC isolation network provides an additional isolation factor at the junction plasma frequency and allows flexibility in the choice of SQUID parameters. Our thin-film on-chip LC isolation network has a 10 nH inductor and an 80 pF capacitor. The combination of the broadband filter and LC filter provides a maximum nominal isolation factor of about 108 at a qubit plasma frequency of about 6.7 GHz. To reduce dielectric loss and two level systems in the qubit junction, we use a relatively small area (4 mum2) Al/AlOx/Al qubit junction built on sapphire and add an external capacitor with 100 nm thick SiNx dielectric layers. Measurements revealed Rabi oscillations with an envelope decay time constant of about 42 ns, and an energy relaxation time of 32 ns, consistent with a loss tangent tan(delta)=7times10-4 in the SiNx.

Quantum behavior of a dc SQUID phase qubit

We analyze the behavior of a dc superconducting quantum interference device phase qubit in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias leads. Ignoring dissipation, we find the two-dimensional Hamiltonian of the system and use numerical methods and a cubic approximation to solve Schr\"odinger's equation for the eigenstates, energy levels, tunneling rates, and expectation value of the currents in the junctions. Using these results, we investigate how well this design provides isolation while preserving the characteristics of a phase qubit. In addition, we show that the expectation value of current flowing through the isolation junction depends on the state of the qubit and can be used for nondestructive read out of the qubit state.

Strong Tunable Coupling between a Superconducting Charge and Phase Qubit

We have realized a tunable coupling over a large frequency range between an asymmetric Cooper pair transistor (charge qubit) and a dc SQUID (phase qubit). Our circuit enables the independent manipulation of the quantum states of each qubit as well as their entanglement. The measurement of the charge qubit's quantum states is performed by an adiabatic quantum transfer from the charge to the phase qubit. The measured coupling strength is in agreement with an analytic theory including a capacitive and a tunable Josephson coupling between the two qubits.

Pulse Current Measurements and Rabi Oscillations in a dc SQUID Phase Qubit

We have used 2 ns pulses of current to read out the states of a Nb/AlOx/Nb dc SQUID phase qubit at 25 mK. Plotting the number of escape events that occur versus the size of the current pulse reveals a series of steps corresponding to the occupancy of different energy levels. After calibrating the measurement pulses, we fit these steps to determine the population in each level. Rabi oscillations were viewed using this technique. The single-shot measurement fidelity was theoretically analysed and the optimal single pulse in our device was determined.

Increasing Spectroscopic Coherence Times of a DC SQUID Phase Qubit by Operating Deeper in the Potential Well

We present measurements of the spectroscopic coherence time, T2* of a Nb-AlOx-Nb dc SQUID phase qubit. T2* is calculated from the spectroscopic width of the |0rang to |1rang transition measured at 25 mK. We find that T2*increases at higher transition frequencies corresponding to measurements deeper in the potential well. The measured are consistent with root mean square current noise saturating at 4 nA.

Strong-Field Effects in the Rabi Oscillations of the Superconducting Phase Qubit

Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and two-photon Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.