Quantum phase slips (QPS) or the macroscopic quantum tunneling (MQT) of a nanowire’s order parameter through an activation energy barrier have remained the subject of intense debate for many years. They are expected to occur at low enough temperature where thermally activated phase slips (TAPS) have been frozen out in analogy with Josephson junctions where the macroscopic tunneling of phase at low temperatures has been conclusively experimentally demonstrated. We address this question by following a similar experimental strategy to that employed for establishing MQT in JJs. By measuring switching current distributions, we can probe the phase slip rate and determine if it corresponds to thermal activation or quantum tunneling. Having established that the behavior we see is consistent with being in the quantum regime, we can alter properties of the nanowires and see if the response is consistent with the expectations of the quantum model. To do this we employ an in-situ modification technique using high bias voltage pulses. Using these pulses, we can change resistance, critical temperature, critical current and morphology of the nanowire. We can also change the shunting capacitance of the nanowire by altering the photolithography step used to create the nanowires electrodes. The resulting response of the nanowires agrees well with being in the quantum tunneling dominated regime. An interesting side benefit of the pulsing technique is that we can exactly set the nanowires switching current to a desired value. This may be instrumental in the development of superconducting nanowire qubits.
Quantum phase slips (QPS) or the macroscopic quantum tunneling (MQT) of a nanowire’s order parameter through an activation energy barrier have remained the subject of intense debate for many years. They are expected to occur at low enough temperature where thermally activated phase slips (TAPS) have been frozen out in analogy with Josephson junctions where the macroscopic tunneling of phase at low temperatures has been conclusively experimentally demonstrated. We address this question by following a similar experimental strategy to that employed for establishing MQT in JJs. By measuring switching current distributions, we can probe the phase slip rate and determine if it corresponds to thermal activation or quantum tunneling. Having established that the behavior we see is consistent with being in the quantum regime, we can alter properties of the nanowires and see if the response is consistent with the expectations of the quantum model. To do this we employ an in-situ modification technique using high bias voltage pulses. Using these pulses, we can change resistance, critical temperature, critical current and morphology of the nanowire. We can also change the shunting capacitance of the nanowire by altering the photolithography step used to create the nanowires electrodes. The resulting response of the nanowires agrees well with being in the quantum tunneling dominated regime. An interesting side benefit of the pulsing technique is that we can exactly set the nanowires switching current to a desired value. This may be instrumental in the development of superconducting nanowire qubits.
In quasi-one-dimensional nanowires, superconductivity is destroyed by phase slip events. Phase slips can be caused by thermal activation over a free energy barrier (TAPS) or quantum tunneling through the barrier (QPS). Quantum phase slip is an example of macroscopic quantum tunneling. Here, we report the observation of QPS experimentally separated from interference of TAPS in aluminum nanowires. This separation between the low-temperature QPS and the high-temperature TAPS regions is made possible by a phase slip free superconducting region stabilized by the dissipative environment viz. the normal electrodes. Individual QPSs are detected by means of a single-shot voltage measurement protocol, in which they appear as stochastic switching events from the superconducting to the normal state.
We present a detailed report of microwave irradiation of ultranarrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous-wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and, thus, lead to the development of a QPS-based quantum current standard.
Abstract Quantum phase slip (QPS) is the fundamental manifestation of macroscopic quantum tunneling (MQT). We measure the distribution of the switching current I sw in quasi-one-dimensional superconducting NbN nanowires in the temperature range of 0.2–5.1 K. The escape temperature T esc extracted from the I sw distributions exhibits saturation at temperatures below 1.2 K, indicating a transition into the MQT state. We investigate the single-photon response of the nanowire and find that the QPS rate increases with incident light power in the MQT state. We propose the photon-enhanced quantum phase-slip model, which establishes a quantitative relationship between the quantum phase-slip rate and the incident photon energy, generalizing the phase-slip dynamics into the photon-induced non-equilibrium MQT regime.
Quantum phase slippage (QPS) in a superconducting nanowire is a new candidate for developing a quantum bit [Mooij et al. New J. Phys. 2005, 7, 219; Mooij et al. Nat. Phys. 2006, 2, 169; Khlebnikov http://arxiv.org/abs/quant-ph/0210019 2007]. It has also been theoretically predicted that the occurrence of QPS significantly changes the current-phase relationship (CPR) of the wire due to the tunneling between topologically different metastable states [Khlebnikov Phys. Rev. B 2008, 78, 014512]. We present studies on the microwave response of the superconducting nanowires to reveal their CPRs. First, we demonstrate a simple nanowire fabrication technique, based on commercially available adhesive tapes, which allows making thin superconducting wire from different metals. We compare the resistance vs temperature curves of Mo(76)Ge(24) and Al nanowires to the classical and quantum models of phase slips. In order to describe the experimentally observed microwave responses of these nanowires, we use the McCumber-Stewart model [McCumber J. Appl. Phys. 1968, 39, 3113; Stewart Appl. Phys. Lett. 1968, 12, 277], which is generalized to include either classical or quantum CPR.
Macroscopic quantum tunneling is a process by which a macroscopic object, rather than a single electron, tunnels between two macroscopically distinct quantum states. In this dissertation, we will present the study of macroscopic quantum tunneling of phase-slips in superconducting devices, including one-dimensional nanowires, quasi-two-dimensional superconducting strips and doubly connected superconducting devices composed of two nanowires connected in parallel. We observe macroscopic quantum tunneling in these devices by measuring switching current distributions. It is known that the standard deviation of switching current distributions can be measured on a single nanowire to reveal temperatures at which macroscopic quantum tunneling is responsible for phase-slips. Therefore we begin by studying higher moments of the switching current distributions, namely the skewness S (a measure of the asymmetry of a distribution) and kurtosis K (a measure of its peakedness). We find that the skewness and kurtosis of the switching current distributions obtained via the Kurkijarvi process on devices composed of single nanowires do not depend on whether the switching events are initiated by quantum or thermal phase-slips. Skewness and kurtosis deviate considerably from the values associated with a Gaussian distribution (S=0 and K=3). If, in an experiment these higher moments approach Gaussian values they indicate the existence of noise. Next we study macroscopic quantum tunneling of phase-slips in quasi-two-dimensional superconducting strips, which are commercially available devices used as single-photon detectors. These devices are composed of (250 um) long, (120 nm) wide, meandering superconducting strips. Each time a photon with sufficient energy strikes the strip a voltage pulse is produced and counted. However, the accuracy of these detectors is limited by a rate of dark counts (false events). We find that at sufficiently low temperatures, the macroscopic quantum tunneling of a vortex through an edge barrier on the wire (which results in a phase-slip as the vortex crosses the wide wire) contributes a base-level dark count rate in these detectors which must be considered during operation at low enough temperatures. After studying tunneling in single one-dimensional nanowires and wide, quasi-two-dimensional strips, we move our focus to doubly connected superconducting samples composed of two nanowires connected in parallel. We characterize and model these devices, and show their applicability as nanometer-scale superconducting memory cells. We develop precise algorithms allowing us to write and read the information onto such memory cells. We also observe signatures of macroscopic quantum tunneling in these doubly connected devices by observing a saturation in the standard deviation of switching current distributions at low temperatures. We then discuss how macroscopic quantum tunneling of the memory state can lead to a dissipationless operation of the superconducting memory cell. In each of these devices, whether single one-dimensional nanowires, wide quasi-two-dimensional superconducting strips, or two nanowires in parallel, we find, quite surprisingly, that the same equations can be used to model macroscopic quantum tunneling at the high currents we apply. Therefore we argue that the physics of macroscopic quantum tunneling in wide quasi-two-dimensional strips and doubly connected nanowire devices can be well understood in the context of tunneling in a single, one-dimensional nanowire.
In systems with reduced dimensions quantum fluctuations have a strong influence on the electronic conduction, even at very low temperature. In superconductors this is especially interesting, since the coherent state of the superconducting electrons is strongly interacting with these fluctuations and therefore is a sensitive tool to study them. In this paper, we report on comprehensive measurements of superconducting nanowires in the quantum phase slip regime. Using an intrinsic electromigration process, we have developed a method to lower the resistance of lithographically fabricated highly resistive nanowires in situ and in small consecutive steps. At low temperature we observe critical (Coulomb) blockade voltages and superconducting critical currents, depending on the nanowire's normal-state resistance, in good agreement with theoretical models. Between these two regimes, we find a continuous transition displaying a nonlinear metallic-like behavior. The reported intrinsic electromigration technique is not limited to low temperatures as we find a similar change in resistance that spans over three orders of magnitude also at room temperature. Aside from superconducting quantum circuits, such a technique to reduce the resistance may also have applications in modern electronic circuits.