Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

Fink, J. M.; Steffen, L.; Studer, P.; Bishop, Lev S.; Baur, M.; Bianchetti, R.; Bozyigit, Deniz; Lang, C. B.; Filipp, Stefan; Leek, Peter; Wallraff, Andreas

doi:10.1103/physrevlett.105.163601

Cited by 82 publications

(92 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To this end, the second-order correlation function g (2) (τ ) has been measured to analyze the photon statistics of thermal [33][34][35] or quantum [36][37][38] emitters ever since the ground-breaking experiments of Hanbury Brown and Twiss [39,40]. While these experiments use the time delay τ as control parameter, at microwave frequencies the photon number n can be controlled conveniently [15,32,[41][42][43][44]. In the specific case of a thermal field at frequency ω, the Bose-Einstein distribution yields n(T ) = [exp( ω/k B T ) − 1] −1 and Var(n) = n 2 + n, which can be controlled by the temperature T of the emitter.…”

mentioning

confidence: 99%

Photon Statistics of Propagating Thermal Microwaves

et al. 2017

View full text Add to dashboard Cite

In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n 2 + n photon number variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers 0.05 n 1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.As propagating electromagnetic fields in general [1][2][3], propagating microwaves with photon numbers on the order of unity are essential for quantum computation [4,5], communication [6], and illumination [7][8][9][10] protocols. Because of their omnipresence in experimental setups, the characterization of thermal states is especially relevant for many applications [11][12][13][14]. Specifically in the microwave regime, sophisticated experimental techniques for their generation at cryogenic temperatures, their manipulation, and detection have been developed in recent years. In this context, an important aspect is the generation of propagating thermal microwaves using thermal emitters [15][16][17]. These emitters can be spatially separated from the setup components used for manipulation and detection [18,19], which allows one to individually control the emitter and the setup temperature. Due to the low energy of microwave photons, the detection of these fields typically requires the use of nearquantum-limited amplifiers [20][21][22][23], cross-correlation detectors [17, 18, 24], or superconducting qubits [25][26][27][28].The unique nature of propagating fields is reflected in their photon statistics, which is described by a probability distribution either in terms of the number states or in terms of its moments. The former were studied by coupling the field to an atom or qubit and measuring the coherent dynamics [29][30][31] or by spectroscopic analysis [32]. The moment-based approach requires knowledge on the average photon number n and its variance Var(n) = n 2 − n 2 to distinguish many states of interest. To this end, the second-order correlation function g (2) (τ ) has been measured to analyze the photon statistics of thermal [33][34][35] or quantum [36][37][38] emitters ever since the ground-breaking experiments of Hanbury Brown and Twiss [39,40]. While these experiments use the time delay τ as control parameter, at microwave frequencies the photon number n can be controlled conveniently [15,32,[41][42][43][44]. In the specific case of a thermal field at frequency ω, the Bose-Einstein distribution yields n(T ) = [exp( ω/k B T ) − 1] −1 and Var(n) = n 2 + n, which can be controlled by the temperature T of the emitter. In practice, one wants to distinguish this relation from both the classical limit Var(n) = n 2 and the Poissonian behavior Var(n) = n characteristic for coherent states [41] or shot noise [45,46]. Hence, as shown in Fig. 1, the most relev...

show abstract

mentioning

confidence: 99%

Photon Statistics of Propagating Thermal Microwaves

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Such jumps to the bare cavity frequency have been observed before as quantum to classical transitions by applying either high powers of a coherent drive or white noise to the cavity. 32,33 In our experiment the critical power of the drive tone that determines the onset of this quasi-harmonic regime is strongly dependent on the flux-bias point. For driving powers corresponding to less than N d~4 0 intra-cavity photons, the bar-like feature becomes power independent, measured with drive powers as low as N d ≲ 0.04, ruling out a role of the applied drive tone in this feature.…”

Section: Resultsmentioning

confidence: 95%

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

et al. 2017

View full text Add to dashboard Cite

With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency ω a,m and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/ω m = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling. With strong coupling, 3 where the coupling is larger than the dissipation rates γ and κ of the atom and mode respectively, experiments such as photon-number resolution 4 or Schrödinger-cat revivals 5 have beautifully displayed the quantum physics of a single-atom coupled to the electromagnetic field of a single mode. As the field matures, circuits of larger complexity are explored, 6-8 opening the prospect of controllably studying systems that are theoretically and numerically difficult to understand.One example is the interaction between an (artificial) atom and an electromagnetic mode where the coupling rate becomes a considerable fraction of the atomic or mode eigen-frequency. This ultra-strong coupling (USC) regime, described by the quantum Rabi model, shows the breakdown of excitation number as conserved quantity, resulting in a significant theoretical challenge. 9,10 In the regime of g=ω a;m ' 1, known as deep-strong coupling (DSC), a symmetry breaking of the vacuum is predicted 11 (i.e., qualitative change of the ground state), similar to the Higgs mechanism or Jahn-Teller instability. To date, U/DSC with superconducting circuits has only been realized with flux qubits 6,12 or in the context of quantum simulations. 13,14 Using transmon qubits for USC is interesting due to their higher coherence rates 15 as well as their weakly-anharmonic nature, allowing the exploration of a different Hamiltonian than with flux qubits. 16 Since transmon qubits are currently a standard in quantum computing efforts, [17][18][19] implementing USC in a transmon architecture could also have technological applications by

show abstract

“…Thus, a circuit QED system with broken symmetry in the qubit potential energy can be used to easily generate a displaced number state. This can be used to study the boundary between the classical and quantum worlds [78][79][80][81].…”

Section: Discussionmentioning

confidence: 99%

Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields

Zhao

Liu

et al. 2015

Phys. Rev. A

View full text Add to dashboard Cite

Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these classical-field-assisted multiphoton processes of the singlemode cavity field are very similar to those for cold ions, confined to a coaxial RF-ion trap and driven by a classical field. We show that arbitrary superpositions of Fock states can be more efficiently generated using these controllable multiphoton transitions, in contrast to the single-photon resonant transition when there is only a SQ-field transverse coupling. The experimental feasibility for different SQs is also discussed.

show abstract

Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

Cited by 82 publications

References 23 publications

Photon Statistics of Propagating Thermal Microwaves

Photon Statistics of Propagating Thermal Microwaves

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

Generating nonclassical photon states via longitudinal couplings between superconducting qubits and microwave fields

Contact Info

Product

Resources

About