arXiv subjects

J. E. Mooij

Publications and source records attributed to J. E. Mooij.

At least 19 recordsLinked to original sources

arXiv2016

Aluminium-oxide wires for superconducting high kinetic inductance circuits

We investigate thin films of conducting aluminium-oxide, also known as granular aluminium, as a material for superconducting high quality, high kinetic inductance circuits. The films are deposited by an optimised reactive DC magnetron sputter process and characterised using microwave measurement techniques at milli-Kelvin temperatures. We show that, by precise control of the reactive sputter conditions, a high room temperature sheet resistance and therefore high kinetic inductance at low temperatures can be obtained. For a coplanar waveguide resonator with 1.5\,k$Ω$ sheet resistance and a kinetic inductance fraction close to unity, we measure a quality factor in the order of 700\,000 at 20\,mK. Furthermore, we observe a sheet resistance reduction by gentle heat treatment in air. This behaviour is exploited to study the kinetic inductance change using the microwave response of a coplanar wave guide resonator. We find the correlation between the kinetic inductance and the sheet resistance to be in good agreement with theoretical expectations.

cond-mat.supr-con↗

arXiv2016

Broken selection rule in the quantum Rabi model

Understanding the interaction between light and matter is very relevant for fundamental studies of quantum electrodynamics and for the development of quantum technologies. The quantum Rabi model captures the physics of a single atom interacting with a single photon at all regimes of coupling strength. We report the spectroscopic observation of a resonant transition that breaks a selection rule in the quantum Rabi model, implemented using an $LC$ resonator and an artificial atom, a superconducting qubit. The eigenstates of the system consist of a superposition of bare qubit-resonator states with a relative sign. When the qubit-resonator coupling strength is negligible compared to their own frequencies, the matrix element between excited eigenstates of different sign is very small in presence of a resonator drive, establishing a sign-preserving selection rule. Here, our qubit-resonator system operates in the ultrastrong coupling regime, where the coupling strength is 10\% of the resonator frequency, allowing sign-changing transitions to be activated and, therefore, detected. This work shows that sign-changing transitions are an unambiguous, distinctive signature of systems operating in the ultrastrong coupling regime of the quantum Rabi model. These results pave the way to further studies of sign-preserving selection rules in multiqubit and multiphoton models.

quant-ph↗

arXiv2012

Selective darkening of degenerate transitions for implementing quantum controlled-NOT gates

We present a theoretical analysis of the selective darkening method for implementing quantum controlled-NOT (CNOT) gates. This method, which we recently proposed and demonstrated, consists of driving two transversely-coupled quantum bits (qubits) with a driving field that is resonant with one of the two qubits. For specific relative amplitudes and phases of the driving field felt by the two qubits, one of the two transitions in the degenerate pair is darkened, or in other words, becomes forbidden by effective selection rules. At these driving conditions, the evolution of the two-qubit state realizes a CNOT gate. The gate speed is found to be limited only by the coupling energy J, which is the fundamental speed limit for any entangling gate. Numerical simulations show that at gate speeds corresponding to 0.48J and 0.07J, the gate fidelity is 99% and 99.99%, respectively, and increases further for lower gate speeds. In addition, the effect of higher-lying energy levels and weak anharmonicity is studied, as well as the scalability of the method to systems of multiple qubits. We conclude that in all these respects this method is competitive with existing schemes for creating entanglement, with the added advantages of being applicable for qubits operating at fixed frequencies (either by design or for exploitation of coherence sweet-spots) and having the simplicity of microwave-only operation.

quant-ph↗

arXiv2010

Tuned transition from quantum to classical for macroscopic quantum states

The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with basis states having persistent currents of 1$ μ$A carried by a billion electrons. By tuning the tunnel barrier between these states we see a cross-over from quantum to classical. Released from non-equilibrium, the system exhibits spontaneous coherent oscillations. For high barriers the lifetime of the states increases dramatically while the tunneling period approaches the phase coherence time and the classical regime is reached.

cond-mat.mes-hall↗

arXiv2010

Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime

We measure the dispersive energy-level shift of an $LC$ resonator magnetically coupled to a superconducting qubit, which clearly shows that our system operates in the ultrastrong coupling regime. The large mutual kinetic inductance provides a coupling energy of $\approx0.82$~GHz, requiring the addition of counter-rotating-wave terms in the description of the Jaynes-Cummings model. We find a 50~MHz Bloch-Siegert shift when the qubit is in its symmetry point, fully consistent with our analytical model.

cond-mat.supr-con↗

arXiv2010

Strong Coupling of a Quantum Oscillator to a Flux Qubit at its Symmetry Point

A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit whose gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-resonator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency $ν_{osc}$ we find the strongest qubit-resonator coupling ($g/h\sim0.1ν_{\rm osc}$). Here being at resonance coincides with the optimal coherence of the symmetry point. Significant further increase of the coupling is possible.

cond-mat.mes-hall↗

arXiv2010

Selective darkening of degenerate transitions demonstrated with two superconducting quantum bits

Controlled manipulation of quantum states is central to studying natural and artificial quantum systems. If a quantum system consists of interacting sub-units, the nature of the coupling may lead to quantum levels with degenerate energy differences. This degeneracy makes frequency-selective quantum operations impossible. For the prominent group of transversely coupled two-level systems, i.e. qubits, we introduce a method to selectively suppress one transition of a degenerate pair while coherently exciting the other, effectively creating artificial selection rules. It requires driving two qubits simultaneously with the same frequency and specified relative amplitude and phase. We demonstrate our method on a pair of superconducting flux qubits. It can directly be applied to the other superconducting qubits, and to any other qubit type that allows for individual driving. Our results provide a single-pulse controlled-NOT gate for the class of transversely coupled qubits.

cond-mat.supr-con↗

arXiv2010

Low-crosstalk bifurcation detectors for coupled flux qubits

We present experimental results on the crosstalk between two AC-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning of the phase the measured crosstalk is 0.1 % and the correlation between the measurement outcomes is less than 0.05 %. These results show that bifurcative readout provides a reliable and generic approach for multi-partite correlation experiments.

cond-mat.supr-con↗

arXiv2010

QND measurement of a superconducting qubit in the weakly projective regime

Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong back-action. We show that the back-action of a DC-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum non-demolition character, with a QND fidelity of 75 %.

cond-mat.supr-con↗

arXiv2009

One- and two-photon spectroscopy of a flux qubit coupled to a microscopic defect

We observed the dynamics of a superconducting flux qubit coupled to an extrinsic quantum system (EQS). The presence of the EQS is revealed by an anticrossing in the spectroscopy of the qubit. The excitation of a two-photon transition to the third excited state of the qubit-EQS system allows us to extract detailed information about the energy level structure and the coupling of the EQS. We deduce that the EQS is a two-level system, with a transverse coupling to the qubit. The transition frequency and the coupling of the EQS changed during experiments, which supports the idea that the EQS is a two-level system of microscopic origin.

cond-mat.supr-con↗

arXiv2009

Josephson squelch filter for quantum nanocircuits

We fabricated and tested a squelch circuit consisting of a copper powder filter with an embedded Josephson junction connected to ground. For small signals (squelch-ON), the small junction inductance attenuates strongly from DC to at least 1 GHz, while for higher frequencies dissipation in the copper powder increases the attenuation exponentially with frequency. For large signals (squelch-OFF) the circuit behaves as a regular metal powder filter. The measured ON/OFF ratio is larger than 50dB up to 50 MHz. This squelch can be applied in low temperature measurement and control circuitry for quantum nanostructures such as superconducting qubits and quantum dots.

cond-mat.supr-con↗

arXiv2008

Tuning the Gap of a Superconducting Flux Qubit

We experimentally demonstrate the in situ tunability of the minimum energy splitting (gap) of a superconducting flux qubit by means of an additional flux loop. Pulses applied via a local control line allow us to tune the gap over a range of several GHz on a nanosecond timescale. The strong flux sensitivity of the gap (up to 0.7 GHz/mPhi_0) opens up the possibility to create different types of tunable couplings that are effective at the degeneracy point of the qubit. We investigate the dependence of the relaxation time and the Rabi frequency on the qubit gap.

cond-mat.supr-con↗

arXiv2008

Role of relaxation in the quantum measurement of a superconducting qubit using a nonlinear oscillator

We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum non-demolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model to characterize the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.

cond-mat.supr-con↗

arXiv2008

Interqubit coupling mediated by a high-excitation-energy quantum object

We consider a system composed of two qubits and a high-excitation-energy quantum object used to mediate coupling between the qubits. We treat the entire system quantum mechanically and analyze the properties of the eigenvalues and eigenstates of the total Hamiltonian. After reproducing well-known results concerning the leading term in the mediated coupling, we obtain an expression for the residual coupling between the qubits in the off state. We also analyze the entanglement between the three objects, i.e. the two qubits and the coupler, in the eigenstates of the total Hamiltonian. Although we focus on the application of our results to the recently realized parametric-coupling scheme with two qubits, we also discuss extensions of our results to harmonic-oscillator couplers, couplers that are near resonance with the qubits and multi-qubit systems. In particular, we find that certain errors that are absent for a two-qubit system arise when dealing with multi-qubit systems.

cond-mat.supr-con↗

arXiv2006

Quantum non-demolition measurement of a superconducting two-level system

In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system - detector interaction which preserves the eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement. We present experiments in which we perform two consecutive measurements on a quantum two -level system, a superconducting flux qubit, by probing the hysteretic behaviour of a coupled nonlinear resonator. The large correlation between the results of the two measurements demonstrates the QND nature of the readout method. The fact that a QND measurement is possible for superconducting qubits strengthens the notion that these fabricated mesoscopic systems are to be regarded as fundamental quantum objects. Our results are also relevant for quantum information processing, where projective measurements are used for protocols like state preparation and error correction.

cond-mat.supr-con↗

arXiv2006

Low-frequency Noise in Josephson Junctions for Superconducting Qubits

We have studied low-frequency resistance fluctuations in shadow-evaporated Al/AlOx/Al tunnel junctions. Between 300 K and 5 K the spectral density follows a 1/f-law. Below 5 K, individual defects distort the 1/f-shape of the spectrum. The spectral density decreases linearly with temperature between 150 K and 1 K and saturates below 0.8 K. At 4.2 K, the spectral density is about two orders of magnitude lower than expected from a recent survey [D. J. Van Harlingen et al., Phys. Rev. B 70, 064510 (2004)]. Due to the saturation below 0.8 K the estimated qubit dephasing times at 100 mK are only about two times longer than calculated by Van Harlingen et al.

cond-mat.supr-con↗

arXiv2006

Parametric coupling for superconducting qubits

We propose a scheme to couple two superconducting charge or flux qubits biased at their symmetry points with unequal energy splittings. Modulating the coupling constant between two qubits at the sum or difference of their two frequencies allows to bring them into resonance in the rotating frame. Switching on and off the modulation amounts to switching on and off the coupling which can be realized at nanosecond speed. We discuss various physical implementations of this idea, and find that our scheme can lead to rapid operation of a two-qubit gate.

cond-mat.mes-hall↗

arXiv2006

High-contrast dispersive readout of a superconducting flux qubit using a nonlinear resonator

We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87 %; of the missing 13 %, only 3 % is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by the first measurement.

cond-mat.mes-hall↗