Ultimate quantum limit for amplification: a single atom in front of a mirror

  1. Emely Wiegand,
  2. Ping-Yi Wen,
  3. Per Delsing,
  4. Io-Chun Hoi,
  5. and Anton Frisk Kockum
We investigate three types of amplification processes for light fields coupling to an atom near the end of a one-dimensional semi-infinite waveguide. We consider two setups where a
drive creates population inversion in the bare or dressed basis of a three-level atom and one setup where the amplification is due to higher-order processes in a driven two-level atom. In all cases, the end of the waveguide acts as a mirror for the light. We find that this enhances the amplification in two ways compared to the same setups in an open waveguide. Firstly, the mirror forces all output from the atom to travel in one direction instead of being split up into two output channels. Secondly, interference due to the mirror enables tuning of the ratio of relaxation rates for different transitions in the atom to increase population inversion. We quantify the enhancement in amplification due to these factors and show that it can be demonstrated for standard parameters in experiments with superconducting quantum circuits.

Scalable collective Lamb shift of a 1D superconducting qubit array in front of a mirror

  1. Kuan-Ting Lin,
  2. Ting Hsu,
  3. Chen-Yu Lee,
  4. Io-Chun Hoi,
  5. and Guin-Dar Lin
We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line.
Similarly to the atomic cases, RDDI comes from exchange of virtual photons of the unexcited modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located elsewhere. This directly signals the interplay of virtual photon processes and explicitly demonstrates the CLS. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved.

Microwave Quantum Optics with an Artificial Atom

  1. Io-Chun Hoi,
  2. C.M. Wilson,
  3. Göran Johansson,
  4. Joel Lindkvist,
  5. Borja Peropadre,
  6. Tauno Palomaki,
  7. and Per Delsing
We address the recent advances on microwave quantum optics with artificial atoms. This field relies on the fact that the coupling between a superconducting artificial atom and propagating
microwave photons in a 1D open transmission line can be made strong enough to observe quantum coherent effects, without using any cavity to confine the microwave photons. We investigate the scattering properties in such a system with resonant coherent microwaves. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. By applying two resonant tones, we also observe the Autler-Townes splitting. By exploiting these effects, we demonstrate two quantum devices at the single-photon level in the microwave regime: the single-photon router and the photon-number filter. These devices provide essential steps towards the realization of an on-chip quantum network.

Breakdown of the cross-Kerr scheme for Photon Counting

  1. Bixuan Fan,
  2. Anton F. Kockum,
  3. Joshua Combes,
  4. Göran Johansson,
  5. Io-chun Hoi,
  6. Christopher Wilson,
  7. Per Delsing,
  8. G. J. Milburn,
  9. and Thomas M. Stace
We show, in the context of single photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarisability
model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single photon applications. Our results are presented in the context of a transmon in a one dimensional microwave waveguide, but the conclusions also apply to optical systems.