Nonlinear response of the vacuum Rabi resonance

Abstract

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics 1,2 has been reached for real atoms in optical cavities 3 , and for artificial atoms in circuit quantum electrodynamics 4 and quantum dot systems 5,6 . A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity, an effect known as vacuum Rabi splitting. The circuit quantum electrodynamics architecture is ideally suited for going beyond this linear-response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet and the appearance of extra peaks with the characteristic √ n spacing of the Jaynes-Cummings ladder. These findings constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Circuit quantum electrodynamics (QED) realizes the coupling between a superconducting qubit and the microwave field inside an on-chip transmission-line resonator 4,7 . The drastic reduction in mode volume for such a quasi-one-dimensional system 8,9 , the recent improvement in coherence times 10 and the absence of atomic motion render circuit QED an ideal system for studying the strong-coupling limit. In the customary linear-response measurement of the transmitted microwave radiation, the vacuum Rabi splitting manifests itself as an avoided crossing between the qubit and the resonator.It may be argued that the observation of the splitting is not yet a clear sign for quantum behaviour 11,12 , because avoided crossings are also ubiquitous in classical physics. However, quantum mechanics gives rise to a distinct anharmonicity of these splittings when initializing the resonator in a higher photon Fock state: when the resonator mode is occupied by n photons, the splitting is enhanced by a factor √ n + 1 as compared with the vacuum Rabi situation. This anharmonicity has been observed with single atoms in both microwave 13 and optical cavities 14,15 . In circuit QED, this characteristic trait has been observed in time-domain measurements 16 . In a system similar to ours, the position of the n = 2 peaks was recently demonstrated in a two-tone pump-probe measurement 17 .Here, we present a theoretical analysis and experimental investigation of the vacuum Rabi resonance in a circuit QED system, where we study the √ n anharmonicity up to n = 5 by exploring the power dependence of the heterodyne transmission (see the Methods section). This type of detection is particularly simple, because it is a continuous measurement involving only a single dr...

Observation of squeezed light from one atom excited with two photons

“…Furthermore, recent theoretical and experimental progress, e.g. [30] indicate that such experiments could soon be transposed to microwave systems using Josephson junctions coupled to strip-line resonators [19][20][21], where even stronger nonlinearities could be achieved. …”

“…In sharp contrast to the emission of single photons [16], the squeezed light stems from the quantum coherence of photon pairs emitted from the system [17]. The ability of a single atom to induce strong coherent interactions between propagating photons opens up new perspectives for photonic quantum logic with single emitters [18][19][20][21][22][23].Unlike in a standard Kerr medium, our squeezing does not result from a simple nonlinear polarization of the medium but from a cavity-enhanced atomic coherence which exists for weak coherent driving. Consider a twostate atom with ground and excited states |g and |e .…”

Circuit quantum electrodynamics in the ultrastrong-coupling regime

“…In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost. This important regime has been reached both in cavity and circuit QED, but the design flexibility and engineering potential of the latter allowed for increasing the ratio between the atom-cavity coupling rate g and the cavity transition frequency ωr above the percent level 8,14,15 . While these experiments are well described by the renowned Jaynes-Cummings model 16 , novel physics is expected when g reaches a considerable fraction of ωr.…”

“…At microwave frequencies, strong coupling is feasible due to the enormous engineerability of superconducting circuit QED systems 4,5 . Here, small cavity mode volumes and large dipole moments of artificial atoms 26 enable coupling rates g of about 15 1 % of the cavity mode frequency ω r . Nevertheless, as in cavity QED, the quantum dynamics of these systems follows the Jaynes-Cummings model, which describes the coherent exchange of a single excitation between the atom and the cavity mode.…”

Three-dimensional cavity-assisted spontaneous emission as a single-photon source: Two cavity modes and Rabi resonance

“…In particular, in this case both spectra of the resonant and the off-resonant modes exhibit threepeak structures. This is an example of the well-known Rabi resonance scenario [34,35], which shows that mode interaction in the bimodal cQED systems may drastically change the features of the nonclassical radiation field emission. In particular, as an important effect of the assisted Rabi resonance we observe at the Rabi resonance frequency region drastic enhancement of the emission spectrum of the off-resonant mode.…”