Anharmonicity of the vacuum Rabi peaks in a many-atom system

Gripp, J.; Mielke, S. L.; Orozco, L. A.; Carmichael, H. J.

doi:10.1103/physreva.54.r3746

Cited by 57 publications

(47 citation statements)

References 14 publications

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“…(32) [61]. The Kerr nonlinearity pulls the vacuum Rabi resonances toward line center, eventually inducing a large enough tilt to recast each as a bistable "switch"-so each vacuum Rabi resonance exhibits hysteresis as the drive detuning is scanned [62]. Figure 4(a) shows an example of dispersive bistability like this, where jαj 2 -the mean-field photon number-is plotted from Eq.…”

Section: B Comparison With Mean-field Theorymentioning

confidence: 98%

Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions

2015

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The Jaynes-Cummings model with coherent drive is considered as an example of a nonlinear oscillator exhibiting photon blockade, where blockade by one, two, three, etc., photons occurs at a sequence of multiphoton absorption resonances. It is shown that with increasing drive strength, the blockade breaks down by way of a dissipative quantum phase transition. The transition is first order, except at a critical point in the space of drive amplitude and detuning, where a continuous transition is observed. Numerical solutions to the quantum master equation in the steady state are presented and compared with mean-field treatments based on Jaynes and Cummings' semiclassical equations (strong coupling with conserved pseudospin) and the Maxwell-Bloch equations (spontaneous emission included). The concept of a "thermodynamic limit" in the absence of conserved particle number is explored. Contrasting the identity of large photon number with weak coupling (large volume) in other dissipative quantum phase transitions for photons (e.g., in the phase-transition analogy of laser threshold), the limit of large photon numbers is a strong-coupling limit.

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Section: B Comparison With Mean-field Theorymentioning

confidence: 98%

Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions

2015

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“…, 5 photons has been recently performed 19 ͑see also Ref. 24 for a multiatom experiment͒. In such a case, multiphoton transmission experiments can probe the energy difference between the E m n max and E 0 0 ͓of Eq.…”

Section: Photon Transmission Spectra: a Quantum To Classical Transmentioning

confidence: 99%

Magnetic strong coupling in a spin-photon system and transition to classical regime

et al. 2010

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We study the energy level structure of the Tavis-Cumming model applied to an ensemble of independent magnetic spins s =1/ 2 coupled to a variable number of photons. Rabi splittings are calculated and their distribution is analyzed as a function of photon number n max and spin system size N. A sharp transition in the distribution of the Rabi frequency is found at n max Ϸ N. The width of the Rabi frequency spectrum diverges as ͱ N at this point. For increased number of photons n max Ͼ N, the Rabi frequencies converge to a value proportional to ͱ n max . This behavior is interpreted as analogous to the classical spin-resonance mechanism where the photon is treated as a classical field and one resonance peak is expected. We also present experimental data demonstrating cooperative, magnetic strong coupling between a spin system and photons, measured at room temperature. This points toward quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques.

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“…That there is a difference between photon counting and heterodyne detection is a characteristic of a single qubit. For a many-qubit system, both types of measurement would typically give the same result, and this many-qubit nonlinear response would be rather different to the single-qubit case, developing first as a frequency pulling and eventually yielding hysteresis 23 .…”

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confidence: 99%

Nonlinear response of the vacuum Rabi resonance

et al. 2008

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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...

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Anharmonicity of the vacuum Rabi peaks in a many-atom system

Cited by 57 publications

References 14 publications

Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions

Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions

Magnetic strong coupling in a spin-photon system and transition to classical regime

Nonlinear response of the vacuum Rabi resonance

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