We present measurements of the dynamics of a polarized magnetic environment coupled to the flux degree of freedom of rf-SQUID flux qubits. The qubits are used as both sources of polarizing field and detectors of the environmental polarization. We probe dynamics at timescales from 5 $μ$s to 5 ms and at temperatures between 12.5 and 22 mK. The measured polarization versus temperature provides strong evidence for a phase transition at a temperature of $5.7\pm 0.3$ mK. Furthermore, the environmental polarization grows initially as $\sqrt{t}$, consistent with spin diffusion dynamics. However, spin diffusion model deviates from data at long timescales, suggesting that a different phenomenon is responsible for the low-frequency behavior. A simple $1/f$ model can fit the data at all time scales but it requires empirical low- and high-frequency cutoffs. We argue that these results are consistent with an environment comprised of random clusters of spins, with fast spin diffusion dynamics within the clusters and slow fluctuations of the total moments of the clusters.
We measure the maximal distance at which two absorbed photons can jointly trigger a detection event in NbN nanowire superconducting single photon detector (SSPD) microbridges by comparing the one-photon and two-photon efficiency of bridges of different overall lengths, from 0 to 400 nm. We find a length of $23 \pm 2$ nm. This value is in good agreement with to size of the quasiparticle cloud at the time of the detection event.
We study the conditions for the probing of an environment affecting one party of a bipartite system of interacting objects by measurements operated only on the other element. We show that entanglement plays no crucial role in such an environment-characterization. On the other hand, if an interaction is established between the two parties, information can be reliably gathered. This result holds for both discrete and continuous variables and helps in the interpretation of recent experiments addressing the properties of mesoscopic objects.
We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper [Armour A D and Blencowe M P 2008 New. J. Phys. Submitted]. The implementation is based on the circuit quantum electrodynamics (QED) set-up, with the addition of a mechanical degree of freedom formed out of a suspended, doubly-clamped segment of the superconducting loop of a dc SQUID located directly opposite the centre conductor of a coplanar waveguide (CPW). The relative merits of two SQUID based qubit realizations are addressed, in par…
A coupled system of a superconducting transmission line resonator with a semiconductor double quantum dot is analyzed. We simulate the phase shift of the microwave signal in the resonator, which is sensitive to the quantum dot qubit state and manipulation. The measurement quality is sufficiently high and the results demonstrate a solid-state quantum processor based on this type of circuit can be envisioned.
We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a …
We experimentally investigate the detection mechanism in a meandered molybdenum silicide (MoSi) superconducting nanowire single-photon detector by characterising the detection probability as a function of bias current in the wavelength range of 750 to 2050 nm. Contrary to some previous observations on niobium nitride (NbN) or tungsten silicide (WSi) detectors, we find that the energy-current relation is nonlinear in this range. Furthermore, thanks to the presence of a saturated detection efficiency over the whole range of wavelengths, we precisely quantify the shape of the curves. This allows …
Electron transport through a quantum dot coupled to superconducting leads shows a sharp conductance onset when a quantum dot orbital level crosses the superconducting coherence peak of one lead. We study superconducting single electron transistors in the weak coupling limit by connecting individual gold nanoparticles with aluminum junctions formed by electromigration. We show that the transport features close to the conductance onset threshold can be accurately described by the quantum dot levels' hybridization with the leads, which is strongly enhanced by the divergent density of states at th…
We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave re…
We consider a gas of attractively interacting cold Fermionic atoms which are manipulated by laser light. The laser induces a transition from an internal state with large negative scattering length to one with almost no interactions. The process can be viewed as a tunneling of atomic population between the superconducting and the normal states of the gas. It can be used to detect the BCS-ground state and to measure the superconducting order parameter.
Non-equilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of the dynamical phase transition, merging different concepts of dynamical criticality, are observed by measuring the non-equilibrium order parameter, nonlocal correlations, and the…
Tunneling defects in disordered materials form spurious two-level systems which are a major source of decoherence for micro-fabricated quantum devices. For superconducting qubits, defects in tunnel barriers of submicrometer-sized Josephson junctions couple strongest to the qubit, which necessitates optimization of the junction fabrication to mitigate defect formation. Here, we investigate whether defects appear predominantly at the edges or deep within the amorphous tunnel barrier of a junction. For this, we compare defect densities in differently shaped Al/AlO$_x$/Al Josephson junctions that …
We study spin relaxation and diffusion in an electron-spin ensemble of nitrogen impurities in diamond at low temperature (0.25-1.2 K) and polarizing magnetic field (80-300 mT). Measurements exploit mode- and temperature-dependent coupling of hyperfine-split sub-ensembles to the resonator. Temperature-independent spin linewidth and relaxation time suggest that spin diffusion limits spin relaxation. Depolarization of one sub-ensemble by resonant pumping of another indicates fast cross-relaxation compared to spin diffusion, with implications on use of sub-ensembles as independent quantum memories…
Quantum two-level systems interacting with the surroundings are ubiquitous in nature. The interaction suppresses quantum coherence and forces the system towards a steady state. Such dissipative processes are captured by the paradigmatic spin-boson model, describing a two-state particle, the "spin", interacting with an environment formed by harmonic oscillators. A fundamental question to date is to what extent intense coherent driving impacts a strongly dissipative system. Here we investigate experimentally and theoretically a superconducting qubit strongly coupled to an electromagnetic environ…
We propose a three-terminal structure to probe robust signatures of Majorana zero modes. This structure consists of a quantum dot coupled to the normal metal, s-wave superconducting and Majorana Y-junction leads. The zero-bias differential conductance at zero temperature of the normal-metal lead peaks at $2e^{2}/h$, which will be deflected after Majorana braiding. This quantized conductance can entirely arise from the Majorana-induced crossed Andreev reflection, protected by the energy gap of the superconducting lead. We find that the effect of thermal broadening is significantly suppressed wh…
Operator spreading, often characterized by out-of-time-order correlators (OTOCs), is one of the central concepts in quantum many-body physics. However, measuring OTOCs is experimentally challenging due to the requirement of reversing the time evolution of systems. Here we apply Floquet engineering to investigate operator spreading in a superconducting 10-qubit chain. Floquet engineering provides an effective way to tune the coupling strength between nearby qubits, which is used to demonstrate quantum walks with tunable couplings, reversed time evolution, and the measurement of OTOCs. A clear l…
Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we study the bosonic many-body localization phase transition using the methods of exact diagonalization as well as matrix product state dynamics. We estimate the location of transition separating the ergodic and the many-body localized phases as a function of the disorder strength and the many-body on-site interaction strength. The main difference be…
Prototype Josephson-junction based qubit coherence times are too short for quantum computing. Recent experiments probing superconducting phase qubits have revealed previously unseen fine splittings in the transition energy spectra. These splittings have been attributed to new microscopic degrees of freedom (microresonators), a previously unknown source of decoherence. We show that macroscopic resonant tunneling in the extremely asymmetric double well potential of the phase qubit can have observational consequences that are strikingly similar to the observed data.
Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation by guaranteeing increasingly larger clusters of errors will not cause logical failure - a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here, we report the protection of classical state…
We study the non-Markovianity of the dynamics of open quantum systems focusing on the cases of independent and common environmental interactions. We investigate the degree of non-Markovianity quantified by two distinct measures proposed by Luo, Fu and Song (LFS) and Breuer, Laine and Pillo (BLP). We show that the amount of non-Markovianity, for a single and a pair of qubits, depends on the quantum process, the proposed measure and whether the environmental interaction is collective or independent. In particular, we demonstrate that while the degree of non-Markovianity generally increases with …
We report on the design and performance of a cryogenic (300 mK) near-field scanning microwave microscope. It uses a microwave resonator as the near-field sensor, operating at a frequency of 6 GHz and microwave probing amplitudes down to 100 uV, approaching low enough photon population (N~1000) of the resonator such that coherent quantum manipulation becomes feasible. The resonator is made out of a miniaturized distributed fractal superconducting circuit that is integrated with the probing tip, micromachined to be compact enough such that it can be mounted directly on a quartz tuning-fork, and …
Superconducting cavities with high quality factors play an essential role in circuit quantum electrodynamics and quantum computing. In measurements of the the intrinsic loss rates of high frequency modes, it can be challenging to design an appropriate coupling to the measurement circuit in such a way that the resulting signal is sufficiently strong but also that this coupling does not lead to unwanted loading circuit, obscuring the intrinsic internal loss rates. Here, we propose and demonstrate a spectroscopic probe of high-Q resonators based on the phenomena of electromagnetically-induced tra…
We study the response of a magnetic-field-driven superconducting qubit strongly coupled to a superconducting coplanar waveguide resonator. We observed a strong amplification/damping of a probing signal at different resonance points corresponding to a one and two-photon emission/absorption. The sign of the detuning between the qubit frequency and the probe determines whether amplification or damping is observed. The larger blue detuned driving leads to two-photon lasing while the larger red detuning cools the resonator. Our experimental results are in good agreement with the theoretical model o…
Microwave pulses are used ubiquitously to control and measure qubits fabricated on superconducting circuits. Due to continual environmental coupling, the qubits undergo decoherence both when it is free and during its interaction with the microwave pulse. As quantum logic gates are executed through pulse-qubit interaction, we study theoretically the decoherence-induced effects during the interaction, especially the variations of the pulse, under a dissipative environment with linear spectral distribution. We find that a transmissible pulse of finite width adopts an asymmetric multi-hump shape, …
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 t…
We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated …
In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 90 % can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The qubit coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.
We demonstrate how a superposition of coherent states can be generated for a microwave field inside a coplanar transmission line coupled to a single superconducting charge qubit, with the addition of a single classical magnetic pulse for chirping of the qubit transition frequency. We show how the qubit dephasing induces decoherence on the field superposition state, and how it can be probed by the qubit charge detection. The character of the charge qubit relaxation process itself is imprinted in the field state decoherence profile.
Progress in superconducting qubit experiments with greater numbers of qubits or advanced techniques such as feedback requires faster and more accurate state measurement. We have designed a multiplexed measurement system with a bandpass filter that allows fast measurement without increasing environmental damping of the qubits. We use this to demonstrate simultaneous measurement of four qubits on a single superconducting integrated circuit, the fastest of which can be measured to 99.8% accuracy in 140ns. This accuracy and speed is suitable for advanced multi-qubit experiments including surface c…
We study the use of a pair of qubits as a decoherence probe of a non-trivial environment. This dual-probe configuration is modelled by three two-level-systems which are coupled in a chain in which the middle system represents an environmental two-level-system (TLS). This TLS resides within the environment of the qubits and therefore its coupling to perturbing fluctuations (i.e. its decoherence) is assumed much stronger than the decoherence acting on the probe qubits. We study the evolution of such a tripartite system including the appearance of a decoherence-free state (dark state) and non-Mar…
A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments and provide an overview of …
Probing many-body Bell correlation depth with superconducting qubits
School of Physics, Zhejiang University（浙江大学物理学院）；Center for Quantum Information, IIIS, Tsinghua University（清华大学信息科学技术研究院量子信息中心）；Instituut-Lorentz, Universiteit Leiden（莱顿大学洛伦兹研究所）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙江大学杭州国际科技创新中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Qi Zhi Institute（上海量子科学研究中心）
We study a pair of quantum dot exciton qubits interacting with a number of fluctuating charges that can induce a Stark shift of both exciton transition energies. We do this by solving the optical master equation using a numerical transfer matrix method. We find that the collective influence of the charge environment on the dots can be detected by measuring the correlation between the photons emitted when each dot is driven independently. Qubits in a common charge environment display photon bunching, if both dots are driven on resonance or if the driving laser detunings have the same sense for …
