We present measurements of coherence and successive decay dynamics of higher energy levels of a superconducting transmon qubit. By applying consecutive π pulses for each sequential transition frequency, we excite the qubit from the ground state up to its fourth excited level and characterize the decay and coherence of each state. We find the decay to proceed mainly sequentially, with relaxation times in excess of 20 μs for all transitions. We also provide a direct measurement of the charge dispersion of these levels by analyzing beating patterns in Ramsey fringes. The results demonstrate the feasibility of using higher levels in transmon qubits for encoding quantum information. DOI: 10.1103/PhysRevLett.114.010501 PACS numbers: 03.67.Lx, 05.40.Ca, 85.25.Cp Universal quantum information processing is typically formulated with two-level quantum systems, or qubits [1]. However, extending the dimension of the Hilbert space to a d-level system, or "qudit," can provide significant computational advantages. In particular, qudits have been shown to reduce resource requirements [2,3], improve the efficiency of certain quantum cryptanalytic protocols [4][5][6][7], simplify the implementation of quantum gates [8,9], and have been used for simulating multidimensional quantum-mechanical systems [10]. The superconducting transmon qubit [11] is a quantum LC oscillator with the inductor replaced by a Josephson junction [ Fig. 1(a)]. The nonlinearity of the Josephson inductance renders the oscillator weakly anharmonic, which allows selective addressing of the individual energy transitions and, thus, makes the device well-suited for investigating multilevel quantum systems. The transmon's energy potential is shallower than the parabolic potential of an harmonic oscillator, leading to energy levels that become more closely spaced as energy increases [ Fig. 1(b)]. Although leakage to these levels can be a complication when operating the device as a two-level system [12], the existence of higher levels has proven useful for implementing certain quantum gates [13,14]. Full quantum state tomography of a transmon operated as a three-level qutrit has also been demonstrated [15].In this Letter, we investigate the energy decay and the phase coherence of the first five energy levels of a transmon qubit embedded in a three-dimensional cavity [16]. We find the energy decay of the excited states to be predominantly sequential, with nonsequential decay rates suppressed by 2 orders of magnitude. The suppression is a direct consequence of the parity of the wave functions in analogy with the orbital selection rules governing transitions in natural atoms. We find that the sequential decay rates scale as i, where i ¼ 1; …; 4 is the initial excited state, thus, confirming the radiation scaling expected for harmonic oscillators [17,18]. The decay times remain in excess of 20 μs for all states up to i ¼ 4, making them promising resources for quantum information processing applications. In addition, we characterize the quantum phase coherence of the...

A high-conductivity two-dimensional (2D) hole gas, analogous to the ubiquitous 2D electron gas, is desirable in nitride semiconductors for wide-bandgap p-channel transistors. We report the observation of a polarization-induced high-density 2D hole gas in epitaxially grown gallium nitride on aluminium nitride and show that such hole gases can form without acceptor dopants. The measured high 2D hole gas densities of about 5 × 1013 per square centimeters remain unchanged down to cryogenic temperatures and allow some of the lowest p-type sheet resistances among all wide-bandgap semiconductors. The observed results provide a probe for studying the valence band structure and transport properties of wide-bandgap nitride interfaces.

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