Abstract
Most future quantum devices, including quantum computers, require control that is broadband, meaning that the rate of change of the time-dependent Hamiltonian is as fast or faster than the dynamics it generates. In many areas of quantum physics, including quantum technology, one must include dissipation and decoherence induced by the environment. While Markovian master equations provide the only really efficient way to model these effects, these master equations are derived for constant Hamiltonians (or those with a discrete set of well-defined frequencies). In 2006, Alicky, Lidar, and Zanardi [Phys. Rev. A 73, 052311 (2006)] provided detailed qualitative arguments that Markovian master equations could not describe systems under broadband control. Despite apparently broad acceptance of these arguments, such master equations are routinely used to model precisely these systems. This odd state of affairs is likely due to a lack of quantitative results. Here we perform exact simulations of two- and three-level systems coupled to an oscillator bath to obtain quantitative results. Although we confirm that in general Markovian master equations cannot predict the effects of damping under broadband control, we find that there is a widely applicable regime in which they can. Master equations are accurate for weak damping if both the Rabi frequencies and bandwidth of the control are significantly smaller than the system's transition frequencies. They also remain accurate if the bandwidth of control is as large as the frequency of the driven transition so long as this bandwidth does not overlap other transitions. Master equations are thus able to provide accurate descriptions of many quantum information processing protocols for atomic systems.
Highlights
Quantum systems that are subjected to noise and relaxation processes due to an interaction with their environments are referred to as being open
We plot the accuracy of the Markovian master equation (MME) and adiabatic master equation (AME) for a two-level system driven on resonance with a constant Rabi frequency
We present some results on the accuracy of the MME and AME for a two-level system when the transition frequency is changed with time
Summary
Quantum systems that are subjected to noise and relaxation processes due to an interaction with their environments are referred to as being open. MME’s are still regularly used to do so, and little in the way of quantitative results on this question have been obtained It is not known just how inaccurate MME’s are for modeling time-dependent systems, nor how this accuracy varies with the bandwidth or other characteristics of the control. Both can potentially affect the accuracy of the master equation If both the speed and bandwidth of the control are small compared to the separation of the transition frequencies ωn of a system, we can be confident that any driving that the control applies to one transition will not affect the behavior of other transitions. While we primarily focus here on time-dependent driving, meaning that the control involves coupling the two levels of the transition together, we will give some results on controlling the frequency of the transition
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