Using numerical simulations, we show that two coupled qubits can amplify a weak signal about hundredfold. This can be achieved if the two qubits are biased simultaneously by this weak signal and a strong pump signal, both of which having frequencies close to the inter-level transitions in the system. The weak signal strongly affects the spectrum generated by the strong pumping drive by producing and controlling mixed harmonics with amplitudes of the order of the main harmonic of the strong drive. We show that the amplification is robust with respect to noise, with an intensity of the order of the weak signal. When deviating from the optimal regime (corresponding to strong qubit coupling and a weak-signal frequency equal to the inter-level transition frequency) the proposed amplifier becomes less efficient, but it can still considerably enhance a weak signal (by several tens). We therefore propose to use coupled qubits as a combined parametric amplifier and frequency shifter.
Simulating a system of two driven coupled qubits, we show that the time-averaged probability to find one driven qubit in its ground or excited state can be controlled by an ac drive in the second qubit. Moreover, off-diagonal elements of the density matrix responsible for quantum coherence can also be controlled via driving the second qubit, i.e., quantum coherence can be enhanced by appropriate choice of the bi-harmonic signal. Such a dynamic synchronization of two differently driven qubits has an analogy with harmonic mixing of Brownian particles forced by two signals through a substrate. Nevertheless, the quantum synchronization in two qubits occurs due to multiplicative coupling of signals in the qubits rather than via a nonlinear harmonic mixing for a classical nano-particle.
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