Energy Variance of a Quantum Bit

Gilbert Reinisch (1)

1 LAGRANGE - Joseph Louis LAGRANGE

We show that the energy spectrum of a driven two-level quantum system-or driven quantum bit (qubit)-can be mathematically defined by its two "state energies" as the time derivatives of its large-amplitude, high-frequency internal as well as overall phases. While the mean values of these latter do fit of course Rabi's well-known harmonic (weak drive) as well as anharmonic (strong drive) dynamics, the standard deviations of these both state energies may become comparable to their mean values themselves. This remarkable property, which we check by use of the quantum expectation value of the variance operator, defines a large statistical time-dependent range of available values for the qubit energy in the presence of an external perturbation. We take the example of a recent experiment [Z. Minev et al. Nature, 570, 200 (2019)] and recover by use of the present theory the measured "time-of-flight" values.

Mots clés: Quantum mechanics model; hamiltonian dynamical system; equations of motion; Quantum bits qubits; Rabi oscillations Quantum switch; variance; standard deviation

Domaines: Physique [physics]; Mathématiques [math]

Gilbert Reinisch. Energy Variance of a Quantum Bit. 2022. ⟨hal-03628136v2⟩