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arXiv:0803.1209 · New Journal of Physics

Single-artificial-atom lasing using a voltage-biased superconducting charge qubit

Sahel Ashhab, J. R. Johansson, Alexandre M. Zagoskin, Franco Nori

Published Feb 17, 2009• 60 citations
arXivHTMLPDF

Abstract

We consider a system composed of a single artificial atom coupled to a cavity mode. The artificial atom is biased such that the most dominant relaxation process in the system takes the atom from its ground state to its excited state, thus ensuring population inversion. A recent experimental manifestation of this situation was achieved using a voltage-biased superconducting charge qubit. Even under the condition of 'inverted relaxation', lasing action can be suppressed if the 'relaxation' rate is larger than a certain threshold value. Using simple transition-rate arguments and a semiclassical calculation, we derive analytic expressions for the lasing suppression condition and the state of the cavity in both the lasing and suppressed-lasing regimes. The results of numerical calculations agree very well with the analytically derived results. We start by analyzing a simplified two-level-atom model, and we then analyze a three-level-atom model that should describe accurately the recently realized superconducting artificial-atom laser.

DOI
10.1088/1367-2630/11/2/023030

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We consider a system composed of a single artificial atom coupled to a cavity mode. The artificial atom is biased such that the most dominant relaxation process in the system takes the atom from its ground state to its excited state, thus ensuring population inversion. A recent experimental manifestation of this situation was achieved using a voltage-biased superconducting charge qubit. Even under the condition of 'inverted relaxation', lasing action can be suppressed if the 'relaxation' rate is larger than a certain threshold value. Using simple transition-rate arguments and a semiclassical calculation, we derive analytic expressions for the lasing suppression condition and the state of the cavity in both the lasing and suppressed-lasing regimes. The results of numerical calculations agree very well with the analytically derived results. We start by analyzing a simplified two-level-atom model, and we then analyze a three-level-atom model that should describe accurately the recently realized superconducting artificial-atom laser.
Superconducting quantum bits originally developed for quantum computation have properties similar to real atoms. Because they are micro fabricated circuits, their interaction with electromagnetic radiation can be engineered and effects known from quantum optics may be realized. In this work, a unique lasing scheme exploiting only the lowest two levels of a single artificial atom coupled to a high-quality superconducting resonator is experimentally realized. It is based on the dressing of the atom’s states by a strong signal and the associated rescaling of the relaxation. In addition, basic physical processes are discussed by a separate characterization of the artificial atom, the resonator, and their coupling. A quantum theory including dissipative processes is developed from basic superconducting effects and its applicability demonstrated by a perfect agreement with the experimental results. It gives an illustrative insight into the physics of atom-photon interaction.
A two-level atom illuminated by a laser may be driven into a population-inverted steady state if it is coupled to a cavity. This is a result of the quantum nature of the electromagnetic field and is forbidden by the semiclassical theory. We numerically and analytically analyze this inversion. We find the maximum possible inversion and determine the rate of approach to the steady state. The quantized cavity modifies the electromagnetic vacuum seen by the atom; this connects our work to that on cavity-enhanced spontaneous emission and on dynamical line narrowing. Experimental signatures of the inversion and potential experimental difficulties are considered. For example, neither the presence of many atoms in the mode nor many modes in the cavity destroys the inversion.
Recently, a lasing effect has been observed in a superconducting nanocircuit where a Cooper-pair box, acting as an artificial three-level atom, was coupled to a resonator [O. Astafiev, K. Inomata, A. O. Niskanen, T. Yamamoto, Yu. A. Pashkin, Y. Nakamura, and J. S. Tsai, Nature (London) 449, 588 (2007)]. Motivated by this experiment, we analyze the quantum dynamics of a three-level atom coupled to a quantum-mechanical resonator in the presence of a driving on the cavity within the framework of the Lindblad master equation. As a result, we have access to the dynamics of the atomic level populations and the photon number in the cavity as well as to the output spectrum. The results of our quantum approach agree with the experimental findings. The presence of a fluctuator in the circuit is also analyzed. Finally, we compare our results with those obtained within a semiclassical approximation.
A single superconducting artificial atom can be used for coupling electromagnetic fields up to the single-photon level due to an easily achieved strong coupling regime. Bringing a pair of harmonic oscillators into resonance with the transitions of a three-level atom converts atomic spontaneous processes into correlated emission dynamics. We present the experimental demonstration of two-mode correlated emission lasing in harmonic oscillators coupled via a fully controllable three-level superconducting quantum system (artificial atom). The correlation of emissions with two different colors reveals itself as equally narrowed linewidths and quenching of their mutual phase diffusion. The mutual linewidth is more than 4 orders of magnitude narrower than the Schawlow-Townes limit. The interference between the different color lasing fields demonstrates that the two-mode fields are strongly correlated.
We investigate properties of a two-level atom coupled to a single cavity mode, and driven by a strong, in general off-resonance, external field. The cavity field is tuned to resonance with a Mollow sideband. We show that the steady-state atomic population may be highly (nearly totally) inverted, a phenomenon forbidden in semiclassical theory, and that a strong enhancement of the resonance fluorescence results. This system is suggested as an alternative approach to create the atomic inversion necessary for laser or maser generation without using additional atomic levels. We also investigate properties of the cavity field, derive an analytical expression for the photon number distribution in the good cavity or strong-coupling limit, and discuss the conditions under which this system acts as a single-atom dressed-state laser.
Quantum two-level systems (TLSs) limit the performance of superconducting qubits and superconducting and optomechanical resonators breaking down the coherence and absorbing the energy of oscillations. TLS absorption can be suppressed or even switched to the gain regime by inverting TLS populations. Here we theoretically explore the regime where the full inversion of TLS populations is attained at energies below a pump field quantization energy by simultaneously applying the pump field and the time varying bias. This regime is attained changing the bias sufficiently slowly to fully invert TLS populations when their energies cross resonance with the pump field and sufficiently fast to avoid TLS relaxation between two resonance crossing events. This population inversion is accompanied by a significant red shift of cavity resonance due to quantum level repulsion. The red-shift in frequency serves as a signature of the population inversion, as its re-entrant behavior as function of bias sweep rate and of the magnitude of the pump field allows the determination of the TLSs dipole moment and relaxation time. The predicted behavior is qualitatively consistent with the recent experimental observations in Al superconducting resonators.