Coherent manipulation of Andreev states in superconducting atomic contacts

Abstract

Abstract:Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here, we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasiparticle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup we perform single-shot readout of this "Andreev qubit". We determine its excited state lifetime and coherence time to be in the microsecond range.Quantum jumps and parity switchings are observed in continuous measurements. In addition to possible quantum information applications, such Andreev qubits are a testbed for the physics of single elementary excitations in superconductors. 2The ground state of a uniform superconductor is a many-body coherent state. Microscopic excitations of this superconducting condensate, which can be created for example by the absorption of photons of high enough energy, are delocalized and incoherent because they have energies in a continuum of states. Localized states arise in situations where the superconducting gap Δ or the superconducting phase undergo strong spatial variations: examples include Shiba states around magnetic impurities (1), Andreev states in vortices (2) or in weak links between two superconductors (3). Because they have discrete energies within the gap, Andreev states are expected to be amenable to coherent manipulation (4,5,6,7,8). In the simplest weak link, a single conduction channel shorter than the superconducting coherence length  , there are only two Andreev levels, governed by the transmission probability  of electrons through the channel and the phase difference  between the two superconducting condensates (3). Despite the absence of actual barriers, quasiparticles (bogoliubons) occupying these Andreev levels are localized over a distance  around the weak link by the gradient of the superconducting phase, and the system can be considered an "Andreev quantum dot " (5,6). Figure 1 EE (13,14). The e state can also be reached directly from g by absorption of a photon of energy 2.A EHere we demonstrate experimentally the manipulation of coherent superpositions of states g and , e even if parasitic transitions to o are also observed.3 Atomic-size contacts are suitable systems to address the Andreev physics because they accommodate a small number of short conduction channels (15). We create them using the microfabricated break-junction technique (16). (Fig. 3D). The analysis (23) of this real-time trace yields a parity switching rate of 50kHz (20). 5The coherent manipulation at   of the two-level system formed by g and e is illustrated in Fig. 4. Figure 4A shows the Rabi oscillations between g and e obtained by varying the duration of a driving pulse at frequency 1 ( , )A ff   (Movie S1). Figure 4B shows how the populations of g and e change when the driving pulse frequency ...

Transmission of a microwave cavity coupled to localized Shiba states

“…2 (a)) to survive inside the gap. In this way, the superconducting gap supports two bound states of the same parity, which allows photonic transitions between them [7].…”

“…Notably, in Ref. [7], this resonant coupling has been measured recently by using a circuit quantum electrodynamic setup coupled to an Andreev qubit. …”

“…The state-dependent frequency pull by the artificial atom can be used to entangle the state of the atom with that of the photons that pass through the resonator [11,12]. By choosing an appropriate driving frequency, high efficiency quantum non-demolition readout measurements of the state of the atom can be performed, or alternatively, the state of the atom can be coherently controlled [7].…”

“…On one side of the transition, when the ground state is a doublet, the photonic cavity is insensitive to the presence of the electronic system and the transmission is unaffected, while on the other side of the transition, when the ground state is a singlet, the Shiba states are expected to be responsive when probed by the cavity [7]. We indeed find that, by attaching the cavity to a pair of external transmission lines, both the amplitude and the phase difference between the outgoing and incoming fields carry the fingerprint of the interaction between the cavity and the electronic system, and furthermore one obtains direct information on the energies of the Shiba states.…”

“…In such a hybrid circuit, a microwave coplanar waveguide resonator can act as a data bus between components of the setup. In particular, it has been shown experimentally that an artificial atom, such as a superconducting qubit [2], a quantum dot (QD) [3][4][5][6], an Andreev dot [7], or a double quantum dot [8][9][10] coupled to a photon cavity, produces a measurable effect on the amplitude and phase of the transmitted electromagnetic field, as well as a shift and broadening of the resonant frequency of the cavity. The state-dependent frequency pull by the artificial atom can be used to entangle the state of the atom with that of the photons that pass through the resonator [11,12].…”