We study a superconducting charge qubit coupled to an intensive electromagnetic field and probe changes in the resonance frequency of the formed dressed states. At large driving strengths, exceeding the qubit energy-level splitting, this reveals the well known Landau-Zener-Stuckelberg (LZS) interference structure of a longitudinally driven two-level system. For even stronger drives we observe a significant change in the LZS pattern and contrast. We attribute this to photon-assisted quasiparticle tunneling in the qubit. This results in the recovery of the qubit parity, eliminating effects of quasiparticle poisoning and leads to an enhanced interferometric response. The interference pattern becomes robust to quasiparticle poisoning and has a good potential for accurate charge sensing.
The parity modulation of the ground state of a superconducting island is a direct consequence of the presence of the Cooper pair condensate preferring an even number of charge carriers. The addition energy of an odd, unpaired quasiparticle equals to the superconducting gap, $Δ$, suppressing single electron hopping in the low temperature limit. Controlling the quasiparticle occupation is of fundamental importance for superconducting qubits as single electron tunneling results in decoherence. In particular, topological quantum computation relies on the parity control and readout of Majorana boun…
We have measured the Cooper Pair Transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional SQUID arrays. The transport properties of the CPT in the high impedance limit, Z_env>>R_Q=6.45~kΩ, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the e…
Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2ϕ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate…
We study a Cooper-pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, due to the Coulomb blockade,mediate a supercurrent by coherent co-tunneling of Cooper pairs. We show that the supercurrent resulting from such co-tunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably,this phase offset persists wh…
Controlled Parity of Cooper Pair Tunneling in a Hybrid Superconducting Qubit
Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所量子器件中心）；NNF Quantum Computing Programme, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所NNF量子计算项目）
Parity control of superconducting islands hosting Majorana zero modes (MZMs) is required to operate topological qubits made from proximitized semiconductor nanowires. We, therefore, study parity effects in hybrid InAs-Al single-Cooper-pair transistors (SCPTs) as a first step. In particular, we investigate the gate-charge supercurrent modulation and observe a consistent 2$e$-periodic pattern indicating a general lack of low-energy subgap states in these nanowires at zero magnetic field. In a parallel magnetic field, an even-odd pattern develops with a gate-charge spacing that oscillates as a fu…
We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kHz. We demonstrate that the pair breaking is caused by the backacti…
We show that odd-parity superconductivity occurs in multilayer Rashba systems without requiring spin-triplet Cooper pairs. A pairing interaction in the spin-singlet channel stabilizes the odd-parity pair-density-wave (PDW) state in the magnetic field parallel to the two-dimensional conducting plane. It is shown that the layer-dependent Rashba spin-orbit coupling and the orbital effect play essential roles for the PDW state in binary and tricolor heterostructures. We demonstrate that the odd-parity PDW state is a symmetry-protected topological superconducting state characterized by the one-dime…
We have observed the effect of the Aharonov-Casher (AC) interference on the spectrum of a superconducting system containing a symmetric Cooper pair box (CPB) and a large inductance. By varying the charge $n_{g}$ induced on the CPB island, we observed oscillations of the device spectrum with the period $Δn_{g}=2e$. These oscillations are attributed to the charge-controlled AC interference between the fluxon tunneling processes in the CPB Josephson junctions. Total suppression of the tunneling (complete destructive interference) has been observed for the charge $n_{g}=e(2n+1)$. The CPB in this r…
We evaluate the rates of energy and phase relaxation of a superconducting qubit caused by stray photons with energy exceeding the threshold for breaking a Cooper pair. All channels of relaxation within this mechanism are associated with the change in the charge parity of the qubit, enabling the separation of the photon-assisted processes from other contributions to the relaxation rates. Among the signatures of the new mechanism is the same order of rates of the transitions in which a qubit looses or gains energy.
We reconsider the issue of Berezinskii-Kosterlitz-Thouless (BKT) transition into an insulating state in the Coulomb-dominated Josephson junction arrays. We show that previously predicted picture of the Cooper-pair BKT transtion at T = T_2 is valid only under the condition that T_2 is considerably below the parity-effect temperature (which is usually almost 10 times below the value of superconductive transition temperature), and even in this case it is not a rigorous phase transition but only a crossover, whereas the real phase transition takes place at T_1 = T_2/4. Our theory is in agreement w…
Novel qubits with intrinsic noise protection constitute a promising route for improving the coherence of quantum information in superconducting circuits. However, many protected superconducting qubits exhibit relatively low transition frequencies, which could make their integration with conventional transmon circuits challenging. In this work, we propose and study a scheme for entangling a tunable transmon with a Cooper-pair parity-protected qubit, a paradigmatic example of a low-frequency protected qubit that stores quantum information in opposite Cooper-pair parity states on a superconductin…
We study a time-reversal-invariant topological superconductor island hosting spatially separated Majorana Kramers pairs, with weak tunnel couplings to two s-wave superconducting leads. When the topological superconductor island is in the Coulomb blockade regime, we predict that a Josephson current flows between the two leads due to a non-local transfer of Cooper pairs mediated by the Majorana Kramers pairs. Interestingly, we find that the sign of the Josephson current is controlled by the joint parity of all four Majorana bound states on the island. Consequently, this parity-controlled Josephs…
We present a protected superconducting qubit based on an effective circuit element that only allows pairs of Cooper pairs to tunnel. These dynamics give rise to a nearly degenerate ground state manifold indexed by the parity of tunneled Cooper pairs. We show that, when the circuit element is shunted by a large capacitance, this manifold can be used as a logical qubit that we expect to be insensitive to multiple relaxation and dephasing mechanisms.
The Cooper-pair transistor (CPT), a small superconducting island enclosed between two Josephson weak links, is the atomic building block of various superconducting quantum circuits. Utilizing gate-tunable semiconductor channels as weak links, the energy scale associated with the Josephson tunneling can be changed with respect to the charging energy of the island, tuning the extent of its charge fluctuations. Here, we directly demonstrate this control by mapping the energy level structure of a CPT made of an indium arsenide nanowire (NW) with a superconducting aluminum shell. We extract the dev…
Coupling Majorana fermion excitations to coherent external fields is an important stage towards their manipulation and detection. We analyse the charge and transmon regimes of a topological nano-wire embedded within a Cooper-Pair-Box, where the superconducting phase difference is coupled to the zero energy parity states that arise from Majorana quasi-particles. We show that at special gate bias points, the photon-qubit coupling can be switched off via quantum interference, and in other points it is exponentially dependent on the control parameter $E_J/E_C$. As well as a probe for topological-s…
High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this work, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a $π$-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the …
A striking characteristic of superconducting circuits is that their eigenspectra and intermode coupling strengths are well predicted by simple Hamiltonians representing combinations of quantum circuit elements. Of particular interest is the Cooper-pair-box Hamiltonian used to describe the eigenspectra of transmon qubits, which can depend strongly on the offset-charge difference across the Josephson element. Notably, this offset-charge dependence can also be observed in the dispersive coupling between an ancillary readout mode and a transmon fabricated in the offset-charge-sensitive (OCS) regim…
We report direct detection of charge-tunneling between a quantum dot and a superconducting island through radio-frequency gate sensing. We are able to resolve spin-dependent quasiparticle tunneling as well as two-particle tunneling involving Cooper pairs. The quantum dot can act as an RF-only sensor to characterize the superconductor addition spectrum, enabling us to access subgap states without transport. Our results provide guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the parity-dependent tunneling between dots and islands.
We study a Cooper pair transistor realized by a mesoscopic superconductor island that couples to a pair of $s$-wave superconducting leads. For a trivial island, the critical supercurrent between the leads exhibits a well-known $2e$-periodicity in the island-gate charge. Here, we show that for an island with spatially separated zero-energy Majorana or Andreev bound states the periodicity of the magnitude of the critical supercurrent transitions to $1e$ in the island-gate charge. Moreover, for Andreev bound states the current-phase relation displays a sign reversal when the parity of the charge …
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analysed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off- resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: "step" and "beats"-like behaviours associated with the quantum interference …
