Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\ensuremath{\pi}$ slips of the phase of the order parameter. However, in a finite-length wire, coherent quantum phase slips would manifest themselves simply as shifts of energy levels in the excitation spectrum of an electrical circuit incorporating this wire. The higher the phase slips' probability amplitude, the larger are the shifts. Phase slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slip amplitudes random functions of time, and therefore turn energy level shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a ``slippery'' wire. The slip-induced linewidths, despite being only of order
100kHz, were resolved from the flux-dependent dephasing of the fluxonium qubit.
Quantum computing provides significantly more efficient methods than classical computers for doing rigorous calculations such as encryption, search algorithms, and physical simulations. This is accomplished through the use of qubits which exist in a superposition of multiple states at once allowing for both complex and fast calculations. Environmental fluctuations interfere with these states and resulting in decoherence and dephasing and the break down of the algorithm. One type of qubit is the fluxonium: a superconducting artificial atom derived from the Cooper pair box. The purpose of this project was to analyze the effect of charge noise on the fluxonium qubit which, in the past, has never systematically been done before. Charge noise enters the qubit in the form of 1/f noise resulting in interference with the Cooper pairs, two loosely bound electrons, hopping between the superconducting island and reservoir. A program was developed to simulate the qubit's state over time by solving a stochastic differential Schrodinger equation numerically. The program simulated the noise by using its 1/f power spectrum. Looking into the both its wavefunction and density matrix, its dephasing and decoherence rates were determined for different inductive, capacitive, and Josephson energies. Results will be presented.
Fluxonium qubits employ a chain of
N Josephson junctions in series. We investigate how the charge-noise induced coherence time
T2 of the qubit depends upon
N, holding fixed the chain's effective capacitance and inductance. The pure dephasing rate decreases with
N, but the relaxation rate increases. As a result,
T2 achieves a maximum. The optimal
N can be much smaller than the number typically chosen in experiments, implying that fluxonium qubits can be significantly simplified without compromising performance.
Quasiparticles are a prominent decoherence source in superconducting qubits, but their effects are notoriously difficult to isolate in fluxonium. Unlike the transmon, fluxonium is insensitive to offset charge, precluding charge-parity detection of quasiparticle tunneling. We address this challenge by measuring the excitation and de-excitation rates in a fluxonium qubit under controlled on-chip quasiparticle injection and isolating the quasiparticle-induced contribution by subtracting the background transition rates. We show that to accurately model the external magnetic flux dependence of the quasiparticle-induced transition rates, it is necessary to account for the superconducting gap asymmetry across the Josephson junctions. A comparison between theory and experiment constrains the relative quasiparticle densities in the small junction and the junction array and helps explain previously reported discrepancies between the bounds on the quasiparticle densities inferred for these two circuit elements.
We compute the decoherence caused by
1∕f fluctuations at low frequency
f in the critical current
I0 of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ scales as ${I}_{0}∕\ensuremath{\Omega}\ensuremath{\Lambda}{S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$, where $\ensuremath{\Omega}∕2\ensuremath{\pi}$ is the energy-level splitting frequency,
SI0(1Hz) is the spectral density of the critical-current noise at
1Hz, and $\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{\mid}{I}_{0}d\ensuremath{\Omega}∕\ensuremath{\Omega}d{I}_{0}\ensuremath{\mid}$ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time
t scales as $\mathrm{exp}(\ensuremath{-}{t}^{2}∕2{\ensuremath{\tau}}_{\ensuremath{\phi}}^{2})$ when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in
I0 and area
A, and show that their values of
SI0(1Hz) scale to within a factor of 3 of $[144{({I}_{0}∕\ensuremath{\mu}\mathrm{A})}^{2}∕(\mathcal{A}∕\ensuremath{\mu}{\mathrm{m}}^{2})]{(\mathrm{pA})}^{2}∕\mathrm{Hz}$ at
4.2K. We empirically extrapolate
SI01∕2(1Hz) to lower temperatures using a scaling
T(K)∕4.2. Using this result, we find that the predicted values of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ at
100mK range from $0.8\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, and are usually substantially longer than values measured experimentally at lower temperatures.
We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.