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arXiv:1707.00656 · Physical Review Letters

Realization of a Λ System with Metastable States of a Capacitively Shunted Fluxonium

Nathan Earnest, Srivatsan Chakram, Yao Lu, Nicholas J. Irons, Ravi Naik, N. Leung, Leonidas E. Ocola, David A. Czaplewski, Brian Baker, Jay Lawrence, Jens Koch, David Schuster

Published Apr 13, 2018• 131 citations
arXivHTMLPDF

Abstract

We realize a Λ system in a superconducting circuit, with metastable states exhibiting lifetimes up to 8 ms. We exponentially suppress the tunneling matrix elements involved in spontaneous energy relaxation by creating a "heavy" fluxonium, realized by adding a capacitive shunt to the original circuit design. The device allows for both cavity-assisted and direct fluorescent readouts, as well as state preparation schemes akin to optical pumping. Since direct transitions between the metastable states are strongly suppressed, we utilize Raman transitions for coherent manipulation of the states.

DOI
10.1103/physrevlett.120.150504

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We realize a Λ system in a superconducting circuit, with metastable states exhibiting lifetimes up to 8 ms. We exponentially suppress the tunneling matrix elements involved in spontaneous energy relaxation by creating a "heavy" fluxonium, realized by adding a capacitive shunt to the original circuit design. The device allows for both cavity-assisted and direct fluorescent readouts, as well as state preparation schemes akin to optical pumping. Since direct transitions between the metastable states are strongly suppressed, we utilize Raman transitions for coherent manipulation of the states.
In the past few years there has been an increasing amount of media coverage on quantum computing, largely due to the substantial investment in the superconducting circuit quantum electrodynamics (cQED) technologies by several governments and technology and finance companies throughout the world. Since their inception, superconducting qubits have realized several orders of magnitude improvement in information lifetimes, but individual qubit lifetimes must be further improved to realize a fault-tolerant quantum computer. A critical component of these circuits, which allows quantum states to be addressed, is the non-linear inductive element known as the Josephson junction. In this thesis, we will present experimental studies showing how to design and fabricate the Josephson element to leverage a recently developed `superinductor' as a way to engineer new qubit regimes, such as the heavy fluxonium. We create the heavy fluxonium with a chain of large Josephson junctions and a large shunting capacitor. This shunting capacitor increases the effective mass of a fictitious particle inside the wells of the heavy fluxonium potential energy landscape, giving rise to two characteristically different transitions: intra-well transmon-like plasmon transitions and inter-well fluxon transitions. The fluxon transitions are heavily suppressed by a reduced dipole matrix element realized from the increased effective mass, and result in metastable fluxon transitions, with T1T_1T1​'s as large as 8ms. This qubit design offers the possibility to study qubit interaction with the thermal bath, the implementation of atomic state preparation techniques such as Raman gates, optical pumping and fluorescent style readout, as well as the possibility to make substantial improvements in qubit lifetimes and create protected qubits in the cQED platform.
Three-level Lambda systems provide a versatile platform for quantum optical phenomena such as Electromagnetically Induced Transparency (EIT), slow light, and quantum memory. Such Lambda systems have been realized in several quantum hardware platforms including atomic systems, superconducting artificial atoms, and meta-structures. Previous experiments involving superconducting artificial atoms incorporated coupling to additional degrees of freedom, such as resonators or other superconducting atoms. In this work, we performed an EIT experiment in microwave frequency range utilizing a single Fluxonium qubit within a microwave waveguide. The Lambda system is consisted of two plasmon transitions in combination with one metastable state originating from the fluxon transition. In this configuration, the controlling and probing transitions are strongly coupled to the transmission line, safeguarding the transition between 0 and 1 states, and ensuring the Fluxonium qubit is close to the sweet spot. Our observations include the manifestation of EIT, a slowdown of light with a delay time of 217 ns, and photon storage. These results highlight the potential as a phase shifter or quantum memory for quantum communication in superconducting circuits.
Bosonic codes in superconducting resonators are a hardware-efficient avenue for quantum error correction and benefit from the inherent bias toward relaxation errors provided by long-lived cavities compared to typical superconducting qubits. The required coupling to an ancillary control qubit, however, can negate these benefits by inducing highly detrimental effects such as excess decoherence and undesired nonlinearities. This is exemplified by the typically employed transmon qubit that imposes limits on cavity operations due to its finite lifetime as well as the inevitably induced self-Kerr nonlinearity. An important question is thus whether a cavity-qubit coupling can be realized that offers readout and control capabilities without spoiling the cavity. Here, motivated by its long lifetime and design flexibility of its Hamiltonian, we experimentally investigate the fluxonium as a control qubit for superconducting cavities. We couple a fluxonium qubit to a superconducting resonator in the strong-dispersive regime and use it to measure the coherence and flux-tunable inherited nonlinearities of the resonator. We then demonstrate quantum control of the oscillator by preparing and characterizing resonator Fock states and their superpositions, with fidelities limited by resonator decay in our planar prototype device. Finally, we show that the fluxonium can realize cavity-couplings that eliminate undesirable cavity nonlinearities and reach regimes of suppressed self-Kerr that are inaccessible to transmon-based devices. Our results thus demonstrate the potential of the fluxonium as a high-performance bosonic control qubit for superconducting cavities that can outperform existing transmon-based architectures.
Long-lived transitions occur naturally in atomic systems due to the abundance of selection rules inhibiting spontaneous emission. By contrast, transitions of superconducting artificial atoms typically have large dipoles, and hence their lifetimes are determined by the dissipative environment of a macroscopic electrical circuit. We designed a multilevel fluxonium artificial atom such that the qubit's transition dipole can be exponentially suppressed by flux tuning, while it continues to dispersively interact with a cavity mode by virtual transitions to the noncomputational states. Remarkably, energy decay time T_{1} grew by 2 orders of magnitude, proportionally to the inverse square of the transition dipole, and exceeded the benchmark value of T_{1}>2 ms (quality factor Q_{1}>4×10^{7}) without showing signs of saturation. The dephasing time was limited by the first-order coupling to flux noise to about 4 μs. Our circuit validated the general principle of hardware-level protection against bit-flip errors and can be upgraded to the 0-π circuit [P. Brooks, A. Kitaev, and J. Preskill, Phys. Rev. A 87, 052306 (2013)PLRAAN1050-294710.1103/PhysRevA.87.052306], adding protection against dephasing and certain gate errors.
Interfacing long-lived qubits with propagating photons is a fundamental challenge in quantum technology. Cavity and circuit quantum electrodynamics (cQED) architectures rely on an off-resonant cavity, which blocks the qubit emission and enables a quantum non-demolition (QND) dispersive readout. However, no such buffer mode is necessary for controlling a large class of three-level systems that combine a metastable qubit transition with a bright cycling transition, using the electron shelving effect. Here we demonstrate shelving of a circuit atom, fluxonium, placed inside a microwave waveguide. With no cavity modes in the setup, the qubit coherence time exceeds 50 μs, and the cycling transition's radiative lifetime is under 100 ns. By detecting a homodyne fluorescence signal from the cycling transition, we implement a QND readout of the qubit and account for readout errors using a minimal optical pumping model. Our result establishes a resource-efficient (cavityless) alternative to cQED for controlling superconducting qubits.
The inductively shunted transmon (IST) is a superconducting qubit with exponentially suppressed fluxon transitions and a plasmon spectrum approximating that of the transmon. It shares many characteristics with the transmon but offers charge offset insensitivity for all levels and precise flux tunability with quadratic flux noise suppression. In this work we propose and realize IST qubits deep in the transmon limit where the large geometric inductance acts as a mere perturbation. With a flux dispersion of only 5.1 MHz we reach the 'sweet-spot everywhere' regime of a SQUID device with a stable coherence time over a full flux quantum. Close to the flux degeneracy point the device reveals tunneling physics between the two quasi-degenerate ground states with typical observed lifetimes on the order of minutes. In the future, this qubit regime could be used to avoid leakage to unconfined transmon states in high-power read-out or driven-dissipative bosonic qubit realizations. Moreover, the combination of well controllable plasmon transitions together with stable fluxon states in a single device might offer a way forward towards improved qubit encoding schemes.