Impact of decoherence on internal state cooling using optical frequency combs

Abstract

We discuss femtosecond Raman-type techniques to control molecular vibrations, which can be implemented for internal-state cooling from Feshbach states with the use of optical frequency combs (OFCs) with and without modulation. The technique makes use of multiple two-photon resonances induced by optical frequencies present in the comb. It provides us with a useful tool to study the details of molecular dynamics at ultracold temperatures. In our theoretical model we take into account decoherence in the form of spontaneous emission and collisional dephasing in order to ascertain an accurate model of the population transfer in the three-level system. We analyze the effects of odd and even chirps of the OFC in the form of sine and cosine functions on the population transfer. We compare the effects of these chirps to the results attained with the standard OFC to see if they increase the population transfer to the final deeply bound state in the presence of decoherence. We also analyze the inherent phase relation that takes place owing to collisional dephasing between molecules in each of the states. This ability to control the rovibrational states of a molecule with an OFC enables us to create deeply bound ultra-cold polar molecules from the Feshbach state.Decoherence at ultracold temperatures is a subject of particular interest and importance in light of the development of methods to manipulate ultracold gases, create and control ultracold molecules [1-3], and study ultracold collisions and chemical reactions [4]. Decoherence is inherently present in ultracold dynamics, and we study it semiclassically within the process of creation of diatomic KRb molecules from Feshbach weakly bound states. Experimentally, ultracold polar KRb molecules were obtained using stimulated Raman adiabatic passage (STIRAP) [5]. As a viable substitute to the STIRAP process, we created a method that makes use of optical frequency combs (OFCs) to perform two-photon resonances and transfer population in a stepwise manner from the Feshbach state to the ground, ultracold state. The implementation of an OFC may be beneficial owing to its intrinsic ability to address the manifold of excited states simultaneously. We make use of a standard OFC and one with sinusoidal phase modulation to induce two-photon Raman transitions. Our theory demonstrates that the impact of decoherence may be minimized by implementing the sinusoidally modulated OFC.The standard OFC is generated by the phase-locked pulse train of the formEquation (1) gives a periodic envelope of the field which oscillates with an optical carrier frequency ω L , and k is an integer number. The pulse-train period T is much greater than τ, where τ is an individual pulse duration. A strictly periodic envelope function can be expressed as a power spectrum by the Fourier series, which is a comb of laser frequencies precisely spaced by the pulse-repetition rate ω r equal to 1∕T. Thus, the period of the pulse train determines the spacing between modes in the frequency comb and may be within a 10 ns ti...

Cooling molecular vibrations with shaped laser pulses: optimal control theory exploiting the timescale separation between coherent excitation and spontaneous emission

“…Compared to the earlier theoretical predictions where a single long pulse implemented the complete cooling process [3][4][5], our approach allows for finding femtosecond pulses that can be repeatedly applied, just as is done in the experiments. Note that this is complementary to proposals for utilizing femtosecond frequency combs for cooling [28][29][30] in that it does not require a definite phase relation between pulses. Shaping the pulses using optimal control allows to significantly reduce the number of excitation/spontaneous emission cycles and reach a high purity of the ground-state molecules.…”

Stimulated Raman adiabatic passage with trains of weak pulses*

“…As a versatile spectroscopic tool, optical frequency combs have a broad range of applications including precision optical metrology [22][23][24], atomic clocks [25], coherent control of electronic processes [26], molecular fingerprinting [27], remote molecular detection [28], and biomedical compound analysis [29], to name a few. The direct application of optical frequency combs was also found to be useful in controlling molecular dynamics [30][31][32][33][34].…”

“…In [33,34], an optical frequency comb having sinusoidal modulation across an individual pulse was implemented to perform adiabatic passage from the initial to the ground state in a three-level Λ-system, faster than the decoherence time. The scheme targets a generation of ultracold molecules from the Feshbach state using two-photon Raman transitions.…”

Harmonic spectral modulation of an optical frequency comb to control the ultracold molecules formation

“…The ifold. The second mechanism strongly depends on the period of the pulse train, since the repetition rate determines the one-photon detuning of the optical frequencies [11,12]. When ω 0 − T −1 = ω 31 , dynamics occurs within a quasi-dark state with the excited state manifold insignificantly populated.…”