Quantum Coherence with a Single Cooper Pair

Bouchiat, Vincent; Vion, Denis; Joyez, P.; Estève, D.; Devoret, Michel

doi:10.1238/physica.topical.076a00165

Cited by 509 publications

(449 citation statements)

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“…The energies corresponding to the transmon eigenstates are ω j (j = 0, 1, ...), and they are determined by the Cooper pair box Hamiltonian 21 for given Josephson energy E J and charging energy E C . In the transmon regime considered here, E J /E C 1, the levels form a weakly anharmonic ladder with anharmonicity α = ω 12 − ω 01 ∼ −E C / (where ω ij = ω j − ω i is the transition frequency between levels i and j).…”

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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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Nonlinear response of the vacuum Rabi resonance

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“…Mesoscopic Josephson junctions can be prepared in a controlled superposition of charge states [17,18] and the coherent time evolution in a Josephson charge qubit has been recently observed [5]. These are the first important experimental steps towards the implementation of a solid state quantum computer.…”

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Detection of geometric phases in superconducting nanocircuits

Falci

Fazio

Palma

et al. 2000

Nature

387

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“…The paper Ref. [1] has demonstrated the potential of the single-Cooper-pair box circuit [2] as a charge qubit and thus has attracted renewed attention to this field. The practical realization of the Cooper pair qubit is not, however, simple and the main problems here are the achievement of a reliable readout of the quantum state and an elongation of the decoherence time.…”

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Cooper-pair qubit and Cooper-pair electrometer in one device

Zorin

2002

Physica C: Superconductivity

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An all-superconductor charge qubit enabling a radio-frequency readout of its quantum state is described. The core element of the setup is a superconducting loop which includes the single-Cooperpair (Bloch) transistor. This circuit has two functions: First, it operates as a charge qubit with magnetic control of Josephson coupling and electrostatic control of the charge on the transistor island. Secondly, it acts as the transducer of the rf electrometer, which probes the qubit state by measuring the Josephson inductance of the transistor. The evaluation of the basic parameters of this device shows its superiority over the rf-SET-based qubit setup.PACS numbers: 74.50.+r, 85.25.Na, 03.67.Lx Superconducting structures with small Josephson tunnel junctions serve as a basis for electronic devices operating on single Cooper pairs and possessing remarkable characteristics. The paper Ref.[1] has demonstrated the potential of the single-Cooper-pair box circuit [2] as a charge qubit and thus has attracted renewed attention to this field. The practical realization of the Cooper pair qubit is not, however, simple and the main problems here are the achievement of a reliable readout of the quantum state and an elongation of the decoherence time. For the most part, these two issues are interrelated because a charge detector coupled to the qubit presents the principal source of quantum decoherence.The qubit setup consisting of a Cooper pair box and a capacitively coupled single electron transistor (SET, including the rf-SET [3]) has been extensively explored [4,5,6]. Although a preliminary analysis shows that qubit states can, in principle, be measured in the snapshot regime [6], the 'mismatch' of the charge carriers in the setup components (namely, the incoherent nature of charges in the SET) might lead to an unaccounted enhancement of decoherence in the system. Alternatively, the generic type of Cooper-pair (Bloch-transistor [7]) electrometers made from superconductors [8,9] seems to be quite promising as regards matching with the Cooper pair box. Furthermore, similar to dc-SQUIDs [10] and in contrast to SETs, the resistively shunted Cooper-pair electrometer belongs to the category of perfect (quantumlimited) linear detectors [11,12] and, therefore, can perform continuous measurements of a quantum object [13].Recently, we have proposed an rf-driven single-Cooperpair electrometer [14] whose energy-resolution figure ǫ can approach the standard quantum limit of /2. The transducer of this electrometer is a Bloch transistor inserted into a superconducting loop. The magnitude of the supercurrent circulating in the loop depends on the polarization charge (quasicharge) on the transistor island induced via a coupling capacitance by the charge source, e.g., the qubit.In this paper we present a circuit in which the electrometer's transducer takes over the function of the Cooper pair box (qubit) as well. The device's core el- ement is a superconducting loop including a mesoscopic double Josephson junction with a capacitive gate (transis...

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Quantum Coherence with a Single Cooper Pair

Cited by 509 publications

References 18 publications

Nonlinear response of the vacuum Rabi resonance

Nonlinear response of the vacuum Rabi resonance

Detection of geometric phases in superconducting nanocircuits

Cooper-pair qubit and Cooper-pair electrometer in one device

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