Multiphoton Transitions in a Macroscopic Quantum Two-State System

Abstract

We have observed multiphoton transitions between two macroscopic quantum-mechanical superposition states formed by two opposite circulating currents in a superconducting loop with three Josephson junctions. Resonant peaks and dips of up to three-photon transitions were observed in spectroscopic measurements when the system was irradiated with a strong RF-photon field. The widths of the multiphoton absorption dips are shown to scale with the Bessel functions in agreement with theoretical predictions derived from the Bloch equation or from a spin-boson model. PACS numbers: 74.50.+r, 03.67.Lx, 42.50.Hz, 85.25.Dq A macroscopic quantum two-state system (TSS) offers a unique testing ground for exploring the foundations of quantum mechanics [1]. This system can be in a quantum-mechanical superposition of macroscopically distinct states, and its quantum nature can be revealed by measuring the absorption of an integer number of photons from an externally applied photon field [2]. Since a macroscopic quantum system cannot be completely decoupled from its environment, dissipative and decoherence effects are unavoidable [1,2,3]. In addition to the investigation of fundamental physics, the quantum TSS also serves as an elementary carrier of information in a quantum information processor in the form of a quantum bit (qubit) [4]. Artificially designed superconducting circuits with mesoscopic Josephson junctions constitute an important class of macroscopic quantum systems. The charge degree of freedom of Cooper pairs is used to induce coherent quantum oscillations between two charge states of a Cooper pair box [5]. A circuit with a single relatively large Josephson junction, which is current-biased close to its critical current, forms a so-called Josephson phase qubit [6]. Moreover, three Josephson junctions arranged in a superconducting loop threaded by an externally applied magnetic flux constitute a flux qubit [7]. The device could be prepared in a quantum superposition of two states carrying opposite macroscopic persistent currents [8]. Coherent Rabi oscillations have been reported, when the qubit and the readout device are connected to obtain a large signal [9]. Rabi oscillations have also been observed in a system, where the qubit and the readout device are spatially separated [10]. Since these solid-state devices are thought to be scalable up to a large number of qubits, they are of particular interest in the context of solid-state quantum information processing [11].The energy scale of quantum circuits containing Josephson junctions is in the microwave regime. This property was demonstrated in the current-voltage characteristics of a Josephson junction under microwave irradiation displaying the well-known Shapiro steps [12]. They appear at voltages corresponding to integer multiples of the applied microwave energy. With this phenomenon, the superconductor phase difference at the junction, which is a macroscopic degree of freedom, can be treated as a classical degree of freedom moving in the Josephson potential. In co...

Multiphoton transitions in Josephson-junction qubits (Review Article)

“…Matching of the ground and higher states with the one-photon energy was exploited to probe the upper levels of the Josephson-junction circuits [19][20][21][22][23][24][25][26]. With increasing driving power, the multiphoton excitations were used to study the features of the artificial atoms both for the two-level dynamics [27][28][29][30][31] and when the upper levels were involved [32][33][34][35][36]. For strong driving, the width of the resonance lines periodically tends to zero, which can be described as the destructive Landau-Zener-Stückelberg interference [37].…”

Quantum crossover in moderately damped epitaxial NbN/MgO/NbN junctions with low critical current density

“…We found a phase diffusion regime, with a damping parameter Q ∼ 3 consistent with what observed in various Josephson systems 11 . The possibility to achieve very low critical current densities in moderately damped NbN junctions, combined with their short electron relaxation time τ < 10ps 12 , paves the way to ex- periments aimed at observing extreme multiphoton tunneling quantum effects 13 thus extending studies performed up to now on few photons processes [14][15][16] . The intrinsic properties of low-Jc NbN junctions with maximum critical current I co < 1µA meet the condition τ < /E J = 2e/I co , where E J = I co /2e is the Josephson energy, nominally required to observe multi-photon effects in the presence of a non-stationary signal.…”

Rapid ballistic readout for flux qubits

“…For realistic values of λ J and β the limitation on the fluxon energy (12) is stronger than (6). Since the fluxon size λ J can not be increased much for obvious reasons of convenience of fluxon manipulation, the energy (12) depends only on the junction capacitance C, and can be increased only by decreasing the junction size (see the discussion below).…”

“…Different versions of the qubits which use quantum dynamics of magnetic flux in superconducting loops [1,2,3,4,5,6,7,8,9] are at the moment among the most advanced solid-state qubits. Practically all of them employ the measurement scheme based on the modulation by the measured qubit of the decay rate of the supercurrent of a Josephson junction or a SQUID.…”