**Observation of the Dynamical Casimir Effect and Related Work**

Two parallel mirrors in empty space are attracted to each other due to the vacuum fluctuations of the electromagnetic field, which has a different mode structure inside compared to outside of the mirrors. This striking effect of quantum electrodynamics (QED) was first predicted by Casimir in 1948 and was only experimentally verified more than fifty years later. If instead the mirrors move, there is also a mismatch between vacuum modes at different instances of time. It was predicted 40 years ago that this may result in the creation of real photons out of vacuum fluctuations. This effect is called the dynamical Casimir effect (DCE). Dr.Wilson’s team at Chalmers showed theoretically for the 1st time that changing the electrical length of a transmission line by modulating the parametric inductance of a Josephson junction leads to the DCE [L11, A10]. In a series of experiments, Dr. Wilson’s team experimentally observed the DCE for the first time. In early experiments [L13, L9], the team demonstrated that the nonadiabatic modulation of the electrical length of a microwave cavity, at ~10 GHz, leads to an effective photon-photon interaction that produced photons in the cavity. This was an important first step but, for a variety of reasons, it is difficult to demonstrate in a cavity that the source of the photon generation has a quantum origin. In the 2nd experiment [L6], the team addressed these difficulties by measuring photon generation in an open transmission line, conclusively demonstrating the quantum nature of the effect. An important part of this work was demonstrating that the DCE produces pairs of photons that are correlated, and important resource for quantum communication. In the first experiment in the above series [L9], we further studied the dynamics of parametric oscillations associated with the photon generation. A driven parametric oscillator can exist in a number of qualitatively different dynamical states. We observed all of the states predicted by theory and demonstrated good quantitative agreement between the theoretical predicted and experimentally observed characteristics. We also observed switching of the oscillator between the various dynamical states. These results were an important verification of the general theory of strongly-driven nonlinear systems subject to noise. An enabling step in all of this work was the development of a new technology that continues to enable many fruitful applications in circuit QED (cQED) and elsewhere: tunable superconducting transmission-line resonators [L13]. Tunable resonators with the same architecture have been used by Dr.Wilson’s team and others to make quantum-limited parametric amplifiers and as coupling buses for superconducting qubits.

**Quantum Electrodynamics in 1D**

In a set of experiments, Dr. Wilson’s team studied the strong coupling of a single artificial atom to an open transmission line. This produces an almost ideal 1D quantum electrodynamic system. These first experiments have demonstrated a number of interesting physical effects. For instance, the team demonstrated that the coherent scattering of single photons from the atom leads to the strong extinction (>99%) of the transmitted light, an effect long predicted but never observed in conventional quantum optics [L7]. (This effect was first observed in the same year by Astafiev et al. at NEC.) In the same work, Dr. Wilson’s team demonstrated, for the first time, a rudimentary single-photon router in the microwave regime [L7], an important building block for future quantum networks.

A key requirement of any quantum information network is the ability to generate nonclassical states of the electromagnetic field. In the next experiment with the same quantum system, Dr. Wilson’s team proved that the microwaves scattered from our artificial atom are definitively nonclassical. The team did this by demonstrating photon antibunching in the reflected signal, using a microwave photon statistics analyzer developed in house [L5]. In a third experiment, Dr. Wilson team demonstrated the giant cross-Kerr effect [L1], an effective interaction between two photons mediated by the artificial atom. There has been great interest in the cross-Kerr effect for a number of potential applications such as photonic quantum gates and quantum nondemolition measurements of photons.

**Dressed States and Dressed Decoherence in an Artificial Atom**

Superconducting qubits are an important building block in the field of circuit QED. Dr.Wilson has led a significant effort to study the dressed states of a single-Cooper-pair box (SCB), a type of superconducting qubit, and an intense microwave (~ 7 GHz) field. The dressed states represent the hybridization of the qubit and photon degrees of freedom, and appear as avoided level crossings (ALC) in the combined qubit-photon energy diagram. The ALC occur when the energy of the photons is resonant with the charging energy of the SCB. By embedding the circuit in an rf oscillator (~650 MHz), we can directly probe the dressed states. On resonance, we see that the dressed states absorb energy from the oscillator. When the dressed states are off resonance, we see the dispersive shift of the oscillator frequency. We quantitatively explained both these effects in terms of the Bloch (NMR-like) response of the dressed states driven by the rf probe, allowing us to extract the relaxation and dephasing times of the states. This work was published in L12: PRL 2007.

Working closely with the Chalmers theory group, we have now extended this work to include a microscopic model of relaxation and dephasing in the strongly driven system. Basically, the drive not only dresses the states of the system, but also dresses relaxation and dephasing [A8]. There has been a great deal of theoretical effort to understand this problem, but very little experimental data to compare and contrast with the various theories. We have developed a microscopic model, based on dressed states, that affords a straightforward physical understanding of the complex dynamics of the system. Further, we have demonstrated a good quantitative agreement between our theory and experiments.

**SELECTED REFERENCES**

L1: “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial atom”, I-C Hoi, A.F. Kockum, T. Palomaki, T.M. Stace, B. Fan, L. Tornberg, S.R. Sathyamoorthy, G. Johansson, P.Delsing, C.M. Wilson, Phys. Rev. Letters 111, 053601 (2013).

L2: ”The pumpistor: a linearized model of a flux-pumped dc-SQUID for use as a negative-resistance parametric amplifier”, K.M. Sundqvist, S. Kintas, M. Simoen, P. Krantz, C.M. Wilson and P. Delsing, Applied Physics Letters, accepted for publication (2013).

L3: “Breakdown of the cross-Kerr scheme for Photon Counting”, B. Fan, A.F. Kockum, J. Combes, G. Johansson, I-C Hoi, C.M. Wilson, P. Delsing, G.J. Milburn, T.M. Stace, Phys. Rev. Letters 110, 053601 (2013).

L4. “High Critical-Current Superconductor-InAs Nanowire-Superconductor Junctions” S. Abay, H.A. Nilsson, F. Wu, H.Q. Xu, C.M. Wilson and P. Delsing, NanoLetters 12, (2012).

L5. “Generation of nonclassical microwave states using an artificial atom in 1D open space”, I-C Hoi, T.Palomaki, G. Johansson, J. Lindkvist, P. Delsing, C.M. Wilson, Phys. Rev. Letters 108, 263601 (2012)

L6. “Observation of the dynamical Casimir effect in a superconducting circuit”, C.M. Wilson, G.Johansson, A. Pourkabirian, M. Simoen, J.R. Johansson, F. Nori, & P. Delsing, Nature 479, 376 (2011).

L7. “Demonstration of a Single-Photon Router in the Microwave Regime”, I-C Hoi, C.M. Wilson, G.Johansson, T. Palomaki, B. Peropadre, and P. Delsing, Phys. Rev. Letters 107, 073601 (2011).

L8. “Are `pinholes’ the cause of excess current in superconducting tunnel junctions?”, T. Greibe, M.P.V.Stenberg, C.M. Wilson, T. Bauch, V. Shumeiko, and P. Delsing, Phys. Rev. Lett. 106, 097001 (2011).

L9. “Photon generation in an electromagnetic cavity with a time-dependent boundary”, C.M. Wilson, T.Duty, M. Sandberg, F. Persson, V. Shumeiko, and P. Delsing, Phys. Rev. Letters 105 , 233907 (2010).

L10. “Excess Dissipation in a Single-Electron Box: The Sisyphus Resistance”, F. Persson, C.M. Wilson, M. Sandberg, G. Johansson, and P. Delsing, Nano Letters 10, 953 (2010).

L11. “Dynamical Casimir Effect in a Superconducting Coplanar Waveguide”, J.R. Johansson, G. Johansson, C.M. Wilson and Franco Nori, Physical Review Letters 103, 147003 (2009).

L12. “Coherence Times of Dressed States of a Superconducting Qubit under Extreme Driving”, C.M.Wilson, T. Duty, F. Persson, M. Sandberg, G. Johansson, & P. Delsing, Phys. Rev. Lett. 98, 257003(2007).

L13. “Tuning the field in a microwave resonator faster than the photon lifetime”, M. Sandberg, C.M.Wilson, F. Persson, T. Bauch, V. Shumeiko, G. Johansson, T. Duty, and P. Delsing, Applied Physics Letters 92, 203501 (2008).

L14. “A Radio Frequency Single-Electron Transistor Based on an InAs/InP Heterostructure Nanowire”, H.A. Nilsson, T. Duty, S. Abay, C.M. Wilson, J.B. Wagner, C. Thelander, P. Delsing and L. Samuelson, Nano Letters 8, pp. 872-875 (2008).

A1: “Nonclassical microwave radiation from the dynamical Casimir effect”, J.R. Johansson, G.Johansson, C.M. Wilson, P. Delsing and F. Nori, Physical Review A 87, 043804 (2013).

A2: “Microwave quantum optics with an artificial atom in one-dimensional open space” I.C. Hoi, C.M.Wilson, G. Johansson, J. Lindkvist, B. Peropadre, T. Palomaki and P. Delsing, N. J. Physics 15, 025011 (2013)

A3: “Scattering of coherent states on a single artificial atom”, B. Peropadre, J. Lindkvist, I.C. Hoi, C.M. Wilson, J.J. Garcia-Ripoll, P. Delsing, G. Johansson, N. J. Physics 15, 035009 (2013).

A4: “Approaching perfect microwave photodetection in circuit QED”, B. Peropadre, G. Romero, G.Johansson, C.M. Wilson, E. Solano, J.J. García-Ripoll, Phys. Rev. A 84, 063834 (2011).

A5. “Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator”, P.Bushev, A. Feofanov, H. Rotzinger, I. Protopopov, J.H. Cole, C.M. Wilson, G. Fischer, A. Lukashenko, A. Ustinov, Physical Review B 84, 060501 (2011).

A6. “Fast readout of a single Cooper-pair box using its quantum capacitance”, F. Persson, C.M. Wilson, M. Sandberg and P. Delsing, Physical Review B 82, 134533 (2010).

A7. “Dynamical Casimir effect in superconducting microwave circuits”, J.R. Johansson, G. Johansson, C.M. Wilson and Franco Nori, Physical Review A 82, 052509 (2010).

A8. “Dressed relaxation and dephasing in a strongly driven two-level system”, C.M. Wilson, G.Johansson, T. Duty, F. Persson, M. Sandberg and P. Delsing, Physical Review B 81, 024520 (2010).

A9. “Fast quantum limited readout of a superconducting qubit using a slow oscillator,” Göran Johansson, Lars Tornberg, C.M. Wilson, Physical Review B 74, 100504 (R) (2006).