Rapid biexciton-state preparation in a quantum dot using on-off pulse sequences

Abstract

We consider the problem of pulsed biexciton preparation in a quantum dot and show that a pulse-sequence with a simple on-off-on modulation can achieve complete preparation of the target state faster than the commonly used constant and hyperbolic secant pulses. The durations of the pulses composing the sequence are obtained from the solution of a transcendental equation. Furthermore, using numerical optimal control, we demonstrate that for a wide range of values of the maximum pulse amplitude, the proposed pulse-sequence prepares the biexciton state in the numerically obtained minimum time, for the specific system under consideration. We finally show with numerical simulations that, even in the presence of dissipation and dephasing, high levels of biexciton state fidelity can be generated in short times.

Efficient Biexciton Preparation in a Quantum Dot—Metal Nanoparticle System Using On-Off Pulses

“…while the other potential solution sinωt 1 = 0 leads to a total durations T > π/ω B , as discussed in Ref. [43]. Using Equations ( 21) and ( 23) and the relations cos (θ ± π) = − cos θ, sin (θ ± π) = − sin θ, we end up with the following expression for the total propagator…”

“…To find the minimum possible total duration T = t 1 + t 2 + t 3 such that the π-phase condition is satisfied, we follow Refs. [43,58] and exploit the fact that in each time interval the Hamiltonian of the two-level system is constant. The total propagator U can be decomposed as…”

“…The problem of population transfer from the ground to the biexciton state in a single SQD (without a MNP) has also become the center of immense research activity [ 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ], with potential applications the efficient generation of single photons [ 44 ] and polarization-entangled photons [ 45 , 46 , 47 , 48 , 49 ], processes which can be exploited for various quantum information processing tasks [ 50 ]. A linearly polarized laser pulse is often used to implement the two-photon ground to biexciton transition.…”

“…In this article, we also examine the problem of coherently preparing the biexciton state in a coupled SQD-MNP nanosystem, using on-off pulse-sequences that we have previously derived for an isolated SQD [ 43 ]. We use the three-level quantum cascade model for the SQD and the corresponding modified nonlinear density matrix equations, which also take into account the applied electromagnetic field as well as the interaction between MNP surface plasmons and SQD excitons [ 12 , 17 , 18 , 20 , 54 , 56 ].…”

“…We use the three-level quantum cascade model for the SQD and the corresponding modified nonlinear density matrix equations, which also take into account the applied electromagnetic field as well as the interaction between MNP surface plasmons and SQD excitons [ 12 , 17 , 18 , 20 , 54 , 56 ]. The externally applied field has linear polarization and is at two-photon resonance with the ground to biexciton transition, while the pulses have a simple on-off-on modulation [ 43 ], where the durations of the on-off segments can be found by solving a transcendental equation. These control pulses are derived to quickly accomplish perfect biexciton state preparation in an isolated SQD and in the idealized case where relaxation processes are ignored.…”