We present spectroscopic evidence for the creation of entangled macroscopic quantum states in two current-biased Josephson-junction qubits coupled by a capacitor. The individual junction bias currents are used to control the interaction between the qubits by tuning the energy level spacings of the junctions in and out of resonance with each other. Microwave spectroscopy in the 4 to 6 gigahertzrange at 20 millikelvin reveals energy levels that agree well with theoretical results for entangled states. The single qubits are spatially separate, and the entangled states extend over the 0.7-millimeter distance between the two qubits.

We study the quantum mechanical behavior of a macroscopic, three-body, superconducting circuit. Microwave spectroscopy on our system, a resonator coupling two large Josephson junctions, produced complex energy spectra well explained by quantum theory over a large frequency range. By tuning each junction separately into resonance with the resonator, we first observe strong coupling between each junction and the resonator. Bringing both junctions together into resonance with the resonator, we find spectroscopic evidence for entanglement between all three degrees of freedom, and suggest a new method for controllable coupling of distant qubits, a key step toward quantum computation. The main promise of using solid-state devices for quantum computation [1] is that it will be relatively easy to scale such a technology from an individual qubit to the large number of qubits ultimately required for key applications [2]. A variety of individual qubits based on superconducting devices [3] have been implemented [4,5]. Work has also been reported on entangled states in two coupled charge qubits [6], Josephson-junction phase qubits [7], flux qubits [8], and most recently the coherent dynamics of a flux qubit coupled to its SQUID detector [9]. The next challenge for scaling is to produce the multiparticle entangled states needed for error correction [10] and teleportation [11], preferably in a device that controllably couples distant qubits.A new approach to the scaling of superconducting qubits [12] utilizes an analogy to the strong-coupling regime of atomic cavity-QED experiments [13]. This analogy was recently realized in an elegant experiment [14], in which a single Cooper-pair box qubit (the atom) was capacitively coupled to a superconducting transmission line (the cavity). The sub-µm sized charge qubit was first characterized by measurements of the resonator in the dispersive regime. This was followed by the observation of the resonant vacuum Rabi splitting, a spectroscopic indication of entanglement between the charge qubit and a single photon in the resonator.We present experimental results that extend this new field of superconducting cavity-QED to three macroscopic qubits-two Josephson junctions and a resonator, the analog of two atoms and a cavity. Figure 1 shows a circuit schematic of our system, which consists of two large (10µm × 10µm) Josephson-junction phase qubits connected together by a series inductor-capacitor (LC) resonator. This system is distinct from atomic cavity-QED systems, in that our "atoms" are distinguishable and independently tunable. We first use spectroscopic measurements to study the coupling of each junction to the LC oscillator. We then couple all three degrees of freedom together, and observe spectroscopic evidence in clear agreement with quantum mechanics.The three degrees of freedom of this system are the macroscopic quantum variables γ 1 and γ 2 (the gaugeinvariant phase differences across junctions J1 and J2, respectively), and γ 3 = 2πLI/Φ 0 corresponding to the current I flowing thro...

The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an Al/AlOx/Al Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating AlOx barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc-SQUID driven to its resistive state. The decoherence rates were measured by observing the two-level system's quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge. I: INTRODUCTION While superconducting circuits based on Josephson junctions (JJs) rapidly mature towards favorable and applicable qubits for quantum computers [1-3], a major source of their decoherence traces back to spurious material defects that give rise to the formation of low-energy two-level systems (TLSs). On the other hand, sensitivity to tiny perturbations turns JJ qubits into ideal tools to study the properties of TLSs. For example, microwave spectroscopy of JJ phase qubits shows avoided level crossings revealing the TLSs' quantum character as well as their coherent interaction with the qubit [4]. Various microscopic models including dangling bonds, Andreev bound states [5], and Kondo fluctuators [6] have been suggested to explain the origin of TLSs. There is growing evidence [7, 8], however, that they are formed by small groups of atoms that are able to tunnel between two energetically almost equivalent configurations. This is most strongly supported by recent experiments where the TLSs' energy splittings were tuned by applying external static strain [9]. TLSs are the source of low-energy excitations, which are also responsible for the thermal, acoustic, and dielectric properties of glasses at temperatures below 1 K [10, 11], which are well studied in bulk materials. Inherent to disordered solids, they are present in surface oxides and insulating layers of any microfabricated device as well as in the tunnel barriers of Josephson junctions. In contrast to traditional measurements performed on glasses that probe huge ensembles of TLSs, the sensitivity of JJ-based qubits allows one to address single TLSs and determine their individual properties. Strain-tuning experiments, e.g., measure a TLS's deformation potential [9] and allow for a detailed analysis of the coherent interaction between two TLSs brought into resonance [12]. In another experiment, the temp...

No abstract

We analyze the effect of dissipation and low-frequency current noise on quantum coherence in a currentbiased Josephson junction that has low damping. Developing a stochastic Bloch equation for the reduced density matrix of the system, we determine the resonance response of the system to a weak external microwave current drive. We characterize the response by finding the spectroscopic coherence time T 2 * as a function of the energy relaxation time T 1 and the current noise power spectral density. For current noise with a constant spectral density up to a frequency f c ӷ ͑2T 1 ͒ −1 , we find that the resonance broadening is proportional to the noise spectral density, while for f c Ӷ ͑2T 1 ͒ −1 , the broadening is proportional to the rms current noise. We compare our results to microwave spectroscopy data on 100 m 2 Nb and Al tunnel junctions at milli-Kelvin temperatures and find good agreement between the measured response spectra and our model simulations.

We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.Comment: 4 pages, 6 figures. Slightly Revised and final accepted versio

No abstract

No abstract