Superconductive quantum circuits (SQCs) comprise quantized energy levels that may be coupled via microwave electromagnetic fields. Described in this way, one may draw a close analogy to atoms with internal (electronic) levels coupled by laser light fields. In this Letter, we present a superconductive analog to electromagnetically induced transparency (S-EIT) that utilizes SQC designs of present day experimental consideration. We discuss how S-EIT can be used to establish macroscopic coherence in such systems and, thereby, utilized as a sensitive probe of decoherence.PACS numbers: 42.50.GySuperconductive quantum circuits (SQCs) comprising mesoscopic Josephson junctions can exhibit quantum coherence amongst their macroscopically large degrees of freedom [1]. They exhibit quantized flux and/or charge states depending on their fabrication parameters, and the resultant quantized energy levels are analogous to the quantized internal levels of an atom. Spectroscopy, Rabi oscillation, and Ramsey interferometry experiments have demonstrated that SQCs behave as "artificial atoms" under carefully controlled conditions [2,3,4,5,6,7,8,9]. This Letter extends the SQC-atom analogy to another quantum optical effect associated with atoms: electromagnetically induced transparency (EIT) [10,11]. We propose the demonstration of microwave transparency using a superconductive analog to EIT (denoted S-EIT) in a superconductive circuit exhibiting two meta-stable states (e.g., a qubit) and a third, shorter-lived state (e.g., the readout state). We show that driving coherent microwave transitions between the qubit states and the readout state is a demonstration of S-EIT. We further propose a means to use S-EIT to experimentally probe the qubit decoherence rate in a sensitive manner. The philosophy is similar to that in Ref. 12, where it was proposed to use EIT to measure phase diffusion in atomic Bose-Einstein condensates.The three-level Λ system illustrated in Fig. 1a is a standard energy level structure utilized in EIT [10,11]. It comprises two meta-stable states |1 and |2 , each of which may be coupled to a third excited state |3 . In atoms, the meta-stable states are typically hyperfine or Zeeman levels, while state |3 is an excited electronic state that may spontaneously decay at a relatively fast rate Γ 3 . In an atomic EIT scheme, a resonant "probe" laser couples the |1 ↔ |3 transition, and a "control" laser couples the |2 ↔ |3 transition. The transition coupling strengths are characterized by their Rabi frequencies Ω j3 ≡ −d j3 · E j3 for j = 1, 2 respectively, where d j3 are the dipole matrix elements and E j3 are the slowly varying envelopes of the electric fields. For particular Rabi frequencies Ω j3 , the probe and control fields are effectively decoupled from the atoms by a destructive quantum interference between the states of the two driven transitions. The result is probe and control field transparency [10,11]. In more recent experiments, ultraslow light propagation due to EIT-based refractive index modifications in atomi...

We measured the intrawell energy relaxation time τ d between macroscopic quantum levels in the double well potential of a Nb persistent-current qubit. Interwell population transitions were generated by irradiating the qubit with microwaves. Zero population in the initial well was then observed due to a multi-level decay process in which the initial population relaxed to the lower energy levels during transitions. The qubit's decoherence time, determined from τ d , is longer than 20 µs, holding the promise of building a quantum computer with Nb-based superconducting qubits.

A general method is illustrated to show that the Hamiltonian for circuits of Josephson junctions can he expanded in terms of three Hamiltonians: a Hamiltonian representative of the inductance-free circuit, a Hamiltonian in the form of an harmonic oscillator for the inductance effects of the circulating currents, and a small correction term. This method is used to show that the inductive effects are a small correction to the difference in energy levels in the persistent current qubit.

. (2002). Engineering the quantum measurement process for the persistent current qubit. Physica C: Superconductivity, 368(1). DOI: 10.1016/S0921-4534(01)01184-4 Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractThe SQUID used to measure the flux state of a superconducting flux-based qubit interacts with the qubit and transmits its environmental noise to the qubit, thus causing the relaxation and dephasing of the qubit state. The SQUID-qubit system is analyzed and the effect of the transmittal of environmental noise is calculated. The method presented can also be applied to other quantum systems. Ó

Measurements of thermal activation are made in a superconducting, niobium Persistent-Current (PC) qubit structure, which has two stable classical states of equal and opposite circulating current. The magnetization signal is read out by ramping the bias current of a DC SQUID. This ramping causes time-ordered measurements of the two states, where measurement of one state occurs before the other. This time-ordering results in an effective measurement time, which can be used to probe the thermal activation rate between the two states. Fitting the magnetization signal as a function of temperature and ramp time allows one to estimate a quality factor of 10 6 for our devices, a value favorable for the observation of long quantum coherence times at lower temperatures.