1. Single-artificial-atom lasing using a voltage-biased superconducting charge qubit
S. Ashhab1,2, J. R. Johansson1 , A.M. Zagoskin1,3, and Franco Nori1,2
1Advanced Science Institute, The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama, Japan
2Center for Theoretical Physics, CSCS, Department of Physics, University of Michigan, Ann Arbor, Michigan, USA
3Department of Physics, Loughborough University, Loughborough, UK
Summary
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. Even under this condition, lasing action can be suppressed if the `relaxation' rate, i.e. the pumping rate, is larger than a certain threshold value. Using simple transition-rate arguments, we derive analytic expressions for the lasing suppression condition and the photon-number state of the cavity in both the lasing and suppressed-lasing regimes.
3. Results
1. Circuit and lasing mechanism
Lasing suppression by strong pumping
Even though population inversion is guaranteed in this model (due to the pumping G1 and G2) the lasing can be suppressed if the pumping is too strong. The condition for lasing suppression is
A Cooper pair tunnels from the source to the island.
A Cooper pair is split up and one of the electrons tunnels to the drain.
The remaining unpaired electron tunnels to the drain.
Lasing regime
Using a mean-field approximation and the master equation we can derive the average photon number in the cavity
# Cooper pairs on the island
# unpaired electrons on the island
# electrons that have tunneled to the drain
Thermal regime
Rate equation analysis:
Detailed balance:
Effective thermal-equilibrium state
The atom is biased such that it experiences inverted relaxation from the ground to the excited state.
Comparison between numerical and analytical results
Thermal regime:
2. Hamiltonian and dissipative processes
Jaynes-Cummings Hamiltonian:
Atom
Cavity
Coupling
Lasing regime
Solid lines:
Numerical results
Dashed lines:
Analytical results for the lasing regime
Dotted lines:
Analytical results for the thermal regime
Master equation:
Supported in part by the NSA, LPS, ARO, NSF and JSPS.
arXiv:
Corresponding author: Sahel Ashhab,
= cavity decay rate
G1, G2 = rates of atomic dissipative processes