Abstract
Mechanical oscillators have been demonstrated with very high quality factors over a wide range of frequencies. These also couple to a wide variety of fields and forces, making them ideal as sensors. The realization of a mechanically-based quantum bit could therefore provide an important new platform for quantum computation and sensing. Here we show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit. This can however only be achieved when the device enters the ultrastrong coupling regime. We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and how decoherence from the quantum dot and the mechanical oscillator are inherited by the qubit. Remarkably, the dephasing due to the quantum dot is expected to be reduced by several orders of magnitude in the coupled system. We outline qubit control, readout protocols, the realization of a CNOT gate by coupling two qubits to microwave cavity, and finally how the qubit can be used as a static force quantum sensor.
Highlights
Mechanical systems have important applications in quantum information and quantum sensing—with, for example, significant recent interest in their use for frequency conversion between optical and microwave signals [1,2,3,4,5,6], the sensing of weak forces using position detection at or beyond the standard quantum limit [7], and demonstrations of mechanically based quantum buses and memory elements [8,9,10,11,12]
We show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit
We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and find how decoherence from the quantum dot and the mechanical oscillator is inherited by the qubit
Summary
Mechanical systems have important applications in quantum information and quantum sensing—with, for example, significant recent interest in their use for frequency conversion between optical and microwave signals [1,2,3,4,5,6], the sensing of weak forces using position detection at or beyond the standard quantum limit [7], and demonstrations of mechanically based quantum buses and memory elements [8,9,10,11,12]. The excess electron can sit either on the left or the right dot We show that for sufficiently strong electromechanical coupling, the double quantum dot induces a bistability in the mechanical mode by reducing and changing the sign of the quadratic term of the effective mechanical potential. The two single-charge states, corresponding to an electron on the left or right dot, are coupled by a hopping term t=2. Their relative energy difference ε can be controlled by varying the two gate voltages. In Appendix A, we give a microscopic derivation of the Hamiltonian with the explicit form of the coupling terms
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