Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0701041 · Physical Review Letters

Single-Qubit Lasing and Cooling at the Rabi Frequency

Julian Hauss, Arkady Fedorov, Carsten Hutter, Alexander Shnirman, Gerd Schön

Published Jan 24, 2008• 120 citations
arXivHTMLPDF

Abstract

For a superconducting qubit driven to perform Rabi oscillations and coupled to a slow electromagnetic or nanomechanical oscillator we describe previously unexplored quantum optics effects. When the Rabi frequency is tuned to resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and a bistability with lasing behavior of the oscillator; for red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are minimized. There the system realizes a "single-atom-two-photon laser."

DOI
10.1103/physrevlett.100.037003

Related papers

Dissipation in circuit quantum electrodynamics: lasing and cooling of a low-frequency oscillator

Julian Hauss, Arkady Fedorov, Stephan André +6 more

Superconducting qubits coupled to electric or nanomechanical resonators display effects previously studied in quantum electrodynamics (QED) as well as extensions thereof. Here, we consider a driven qubit coupled to a low-frequency oscillator and study the influence of dissipation. When the qubit is driven to perform Rabi oscillations, with Rabi frequency in resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and lasing behavior of the oscillator ('single-atom laser'). For red detuning, the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit–oscillator coupling is quadratic and decoherence effects are minimized. Here, the system realizes a 'single-atom-two-photon laser'.

arXiv:0806.1298•New Journal of Physics•Sep 30, 2008•49 citations

Decoherence and Relaxation in Driven Circuit QED Systems

Stephan André, Valentina Brosco, Arkady Fedorov +4 more

Recent experiments on quantum state engineering with superconducting circuits realized concepts originally introduced in the field of quantum optics. Motivated by one such experiment we investigate a Josephson qubit coupled to a slow LC oscillator with frequency much lower than the qubit’s energy splitting. The qubit is ac‐driven to perform Rabi oscillations, and the Rabi frequency is tuned to resonance with the oscillator. The properties of this driven circuit QED system depend strongly on relaxation and decoherence effects in the qubit. We investigate both one‐photon and two‐photon qubit‐oscillator coupling, the latter being dominant at the symmetry point of the qubit. When the qubit driving frequency is blue detuned, we find that the system exhibits lasing behavior; for red detuning the qubit cools the oscillator. Similar behavior is expected in an accessible range of parameters for a Josephson qubit coupled to a nano‐mechanical oscillator. In a different parameter regime, furthering the analogies between superconducting and quantum optical systems, we investigate Sisyphus damping, which is the key element of the Sisyphus cooling protocol, as well as its exact opposite, Sisyphus amplification.

AIP conference proceedings•Jan 1, 2008•1 citation

Two-photon lasing by a superconducting qubit

P. Neilinger, Marian Rehak, M. Grajcar +3 more

We study the response of a magnetic-field-driven superconducting qubit strongly coupled to a superconducting coplanar waveguide resonator. We observed a strong amplification/damping of a probing signal at different resonance points corresponding to a one and two-photon emission/absorption. The sign of the detuning between the qubit frequency and the probe determines whether amplification or damping is observed. The larger blue detuned driving leads to two-photon lasing while the larger red detuning cools the resonator. Our experimental results are in good agreement with the theoretical model of qubit lasing and cooling at the Rabi frequency.

arXiv:1501.01543•Physical Review B•Mar 19, 2015•19 citations

Multiphoton transitions in Josephson-junction qubits (Review Article)

Sergey N Shevchenko, A. N. Omelyanchouk, E. V. Il’ichev

Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic \nscale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the \ndistance between the qubit energy levels and their populations and to read out the resonator's state, as well as the \nunavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum \nphenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent \nresults for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC \ncircuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a \nqubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. \nApplication of this theory allows to describe many phenomena for the single and two coupled superconducting \nqubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping \nand amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type \ncharacter, and creation of the inverse population for lasing.

•Jan 1, 2012•41 citations

Few-qubit lasing in circuit QED

Stephan André, Valentina Brosco, Michael Marthaler +2 more

Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic modes in a resonator coupled to a superconducting qubit, we describe the specific mechanisms creating the population inversion, and we study the spectral properties of these systems in the lasing state. Different levels of the theoretical description, i.e. the semi-classical and the semi-quantum approximation, as well as an analysis based on the full Liouville equation are compared. We extend the usual quantum optics description to account for strong qubit–resonator coupling and include the effects of low-frequency noise. Beyond the lasing transition we find for a single- or few-qubit system the phase diffusion strength to grow with the coupling strength, which in turn deteriorates the lasing state.

arXiv:0908.4227•Physica Scripta•Dec 1, 2009•23 citations

Lasing without Inversion in Circuit Quantum Electrodynamics

Michael Marthaler, Yasuhiro Utsumi, Dmitry S. Golubev +2 more

We study the photon generation in a transmission line oscillator coupled to a driven qubit in the presence of a dissipative electromagnetic environment. It has been demonstrated previously that a population inversion in the qubit can lead to a lasing state of the oscillator. Here we show that the circuit can also exhibit the effect of "lasing without inversion." It arises since the coupling to the dissipative environment enhances photon emission as compared to absorption, similar to the recoil effect predicted for atomic systems. While the recoil effect is very weak, and so far elusive, the effect described here should be observable with realistic circuits. We analyze the requirements for system parameters and environment.

arXiv:1012.3557•Physical Review Letters•Aug 23, 2011•48 citations
For a superconducting qubit driven to perform Rabi oscillations and coupled to a slow electromagnetic or nanomechanical oscillator we describe previously unexplored quantum optics effects. When the Rabi frequency is tuned to resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and a bistability with lasing behavior of the oscillator; for red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are minimized. There the system realizes a "single-atom-two-photon laser."
Superconducting qubits coupled to electric or nanomechanical resonators display effects previously studied in quantum electrodynamics (QED) as well as extensions thereof. Here, we consider a driven qubit coupled to a low-frequency oscillator and study the influence of dissipation. When the qubit is driven to perform Rabi oscillations, with Rabi frequency in resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and lasing behavior of the oscillator ('single-atom laser'). For red detuning, the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit–oscillator coupling is quadratic and decoherence effects are minimized. Here, the system realizes a 'single-atom-two-photon laser'.
Recent experiments on quantum state engineering with superconducting circuits realized concepts originally introduced in the field of quantum optics. Motivated by one such experiment we investigate a Josephson qubit coupled to a slow LC oscillator with frequency much lower than the qubit’s energy splitting. The qubit is ac‐driven to perform Rabi oscillations, and the Rabi frequency is tuned to resonance with the oscillator. The properties of this driven circuit QED system depend strongly on relaxation and decoherence effects in the qubit. We investigate both one‐photon and two‐photon qubit‐oscillator coupling, the latter being dominant at the symmetry point of the qubit. When the qubit driving frequency is blue detuned, we find that the system exhibits lasing behavior; for red detuning the qubit cools the oscillator. Similar behavior is expected in an accessible range of parameters for a Josephson qubit coupled to a nano‐mechanical oscillator. In a different parameter regime, furthering the analogies between superconducting and quantum optical systems, we investigate Sisyphus damping, which is the key element of the Sisyphus cooling protocol, as well as its exact opposite, Sisyphus amplification.
We study the response of a magnetic-field-driven superconducting qubit strongly coupled to a superconducting coplanar waveguide resonator. We observed a strong amplification/damping of a probing signal at different resonance points corresponding to a one and two-photon emission/absorption. The sign of the detuning between the qubit frequency and the probe determines whether amplification or damping is observed. The larger blue detuned driving leads to two-photon lasing while the larger red detuning cools the resonator. Our experimental results are in good agreement with the theoretical model of qubit lasing and cooling at the Rabi frequency.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic \nscale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the \ndistance between the qubit energy levels and their populations and to read out the resonator's state, as well as the \nunavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum \nphenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent \nresults for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC \ncircuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a \nqubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. \nApplication of this theory allows to describe many phenomena for the single and two coupled superconducting \nqubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping \nand amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type \ncharacter, and creation of the inverse population for lasing.
Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic modes in a resonator coupled to a superconducting qubit, we describe the specific mechanisms creating the population inversion, and we study the spectral properties of these systems in the lasing state. Different levels of the theoretical description, i.e. the semi-classical and the semi-quantum approximation, as well as an analysis based on the full Liouville equation are compared. We extend the usual quantum optics description to account for strong qubit–resonator coupling and include the effects of low-frequency noise. Beyond the lasing transition we find for a single- or few-qubit system the phase diffusion strength to grow with the coupling strength, which in turn deteriorates the lasing state.
We study the photon generation in a transmission line oscillator coupled to a driven qubit in the presence of a dissipative electromagnetic environment. It has been demonstrated previously that a population inversion in the qubit can lead to a lasing state of the oscillator. Here we show that the circuit can also exhibit the effect of "lasing without inversion." It arises since the coupling to the dissipative environment enhances photon emission as compared to absorption, similar to the recoil effect predicted for atomic systems. While the recoil effect is very weak, and so far elusive, the effect described here should be observable with realistic circuits. We analyze the requirements for system parameters and environment.