Probing Decoherence with Electromagnetically Induced Transparency in Superconductive Quantum Circuits

Abstract

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...

Atomic physics and quantum optics using superconducting circuits

“…This is an important advantage of superconducting circuits compared to natural atoms. EIT using superconducting circuits has been studied theoretically (e.g., [31][32][33]) and experimentally [34,35]. In [35], this phenomenon was experimentally shown using a four-junction loop biased at f = State population inversion and lasing.…”

Electromagnetically Induced Transparency on a Single Artificial Atom

“…EIT related phenomena in superconducting circuits was theoretically studied in Ref. [20].In a few recent experiments multilevel structure of superconducting quantum circuits have been used to demonstrate Autler-Townes splitting and coherent population trapping [21][22][23]. Baur et al observed AutlerTownes splitting in a three level quantum system coupled to a cavity using dispersive measurement.…”

Nanomechanical-resonator-assisted induced transparency in a Cooper-pair box system

“…As a result, the dressed CPB-NR coupled system becomes transparent for a weak signal current with a frequency matching the resonant frequency of CPB qubit. We note that the selection rule here is somewhat different from that of the superconducting flux-qubit circuit, which shows an EIT phenomenon in a configuration [43,44]. There, dipole-like coupling is allowed between all pairs of levels due to the symmetry breaking of the potential of the flux qubit [55].…”

“…In addition to the absorption eliminated via quantum interference, the EIT effect has also been shown to be an active mechanism to slow down or stop a light pulse completely in various systems, such as an ultracold gas of sodium atoms [38], rare-earth-ion-doped crystals [39], semiconductor quantum wells [40], quantum dot exciton systems [41], and systems with four-level or multi-level cells [42]. Recently, it has been proposed to use a superconductive analogy to EIT in a persistent-current flux qubit biased in a configuration to probe small qubit errors due to decoherence or imperfect state preparation [43,44]. Here, we show that the EIT phenomenon could be realized in an effective two-level superconducting CPB charge qubit coupled to an NR.…”