Coherent control of macroscopic quantum states in a single-Cooper-pair box

Coherent control of macroscopic quantum states in a single-Cooper-pair box

February 1, 2008 | Y. Nakamura, Yu. A. Pashkin & J. S. Tsai
A single-Cooper-pair box is a superconducting electrode connected to a reservoir via a Josephson junction, forming an artificial two-level system. It can exhibit coherent superposition of two charge states, making it a candidate for a qubit in quantum computing. This study reports on time-domain observation of coherent quantum-state evolution in the two-level system using a short voltage pulse to control the energy levels. The resulting state was probed by a tunneling current through a probe junction. The results demonstrate coherent operation and measurement of a quantum state in a solid-state device. The system is a unique artificial solid-state system where Cooper pairs form a macroscopic ground state. The only low-energy excitations are transitions between different charge states due to Cooper-pair tunneling. The relative energy of the two levels can be controlled via gate voltage. The system can be considered an effective two-level system by considering the two lowest-energy states differing by one Cooper pair. To investigate coherent evolution, a sharp voltage pulse was applied to control the energy levels and manipulate the quantum state. The pulse brought the two charge states into resonance, allowing coherent evolution between them. The quantum state at the end of the pulse was a superposition of the two charge states, dependent on the pulse length. The probe junction was biased to detect the $ |2\rangle $ state through quasiparticle tunneling events. The experiment showed that the pulse-induced current depends on the pulse length and the dc-induced charge. The current was measured as a function of the pulse length and dc-induced charge, revealing coherent oscillations. The results were compared with simulations of the time-dependent Schrödinger equation, showing good agreement. The study confirms that coherent oscillation can be observed in the time domain and that the quantum state can be controlled through arbitrary pulse lengths. The main decoherence source is spontaneous photon emission, and the decoherence time could exceed 1 μs. The results provide important insights for designing solid-state quantum circuits using superconducting single-Cooper-pair boxes.A single-Cooper-pair box is a superconducting electrode connected to a reservoir via a Josephson junction, forming an artificial two-level system. It can exhibit coherent superposition of two charge states, making it a candidate for a qubit in quantum computing. This study reports on time-domain observation of coherent quantum-state evolution in the two-level system using a short voltage pulse to control the energy levels. The resulting state was probed by a tunneling current through a probe junction. The results demonstrate coherent operation and measurement of a quantum state in a solid-state device. The system is a unique artificial solid-state system where Cooper pairs form a macroscopic ground state. The only low-energy excitations are transitions between different charge states due to Cooper-pair tunneling. The relative energy of the two levels can be controlled via gate voltage. The system can be considered an effective two-level system by considering the two lowest-energy states differing by one Cooper pair. To investigate coherent evolution, a sharp voltage pulse was applied to control the energy levels and manipulate the quantum state. The pulse brought the two charge states into resonance, allowing coherent evolution between them. The quantum state at the end of the pulse was a superposition of the two charge states, dependent on the pulse length. The probe junction was biased to detect the $ |2\rangle $ state through quasiparticle tunneling events. The experiment showed that the pulse-induced current depends on the pulse length and the dc-induced charge. The current was measured as a function of the pulse length and dc-induced charge, revealing coherent oscillations. The results were compared with simulations of the time-dependent Schrödinger equation, showing good agreement. The study confirms that coherent oscillation can be observed in the time domain and that the quantum state can be controlled through arbitrary pulse lengths. The main decoherence source is spontaneous photon emission, and the decoherence time could exceed 1 μs. The results provide important insights for designing solid-state quantum circuits using superconducting single-Cooper-pair boxes.
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