Response to Comment on "Coherent Control of Retinal Isomerization in Bacteriorhodopsin"

Abstract

Joffre attempts to show that the linear response of any quantum system to an external perturbation is phase insensitive, but he uses incorrect mathematical assumptions, misinterprets the time invariance principle, and ignores causality. We argue that the opposite case-an explicit phase dependence for a signal measured in the linear excitation regime-can equally be shown using Joffre's approach and assumptions.T he comment by Joffre (1) claims to make a general statement covering all possible cases of the field-matter interaction in which the measured signal is governed by a twofield interaction. The photoisomerization of retinal in bacteriorhodopsin under question (2), is an example of a strongly coupled system (retinal) to a bath (protein). The system response with respect to photoinduced isomerization necessarily involves at least four modes: a coupling mode, the primary torsional or reactive mode, and dissipation to two accepting modes of the system-bath interaction (3). Joffre attempts to illustrate the general properties of an inherently multilevel problem with a simple two-level system. By definition, this model system cannot properly capture the photoisomerization process. Effectively, Joffre has attempted to treat a multilevel quantum problem without involving quantum mechanics. The derivation and strong assertions of complete generality for a "global system response" function (1) raise many questions that require a more detailed analysis than given to establish their validity.As we show, the outcome for a stationary signal given by equation 3 in (1) is not a unique solution to the problem as formulated (Eq. 1). The method proposed by Joffre allows one to derive an alternative result showing explicitly a phase sensitivity for the measured response. Let us start from equation 1 in (1) for the stationary value of the signal S. In accordance with Joffre, and making use of the hypothesis of time invariance, we replace E(t) by E(t + T), where T is an arbitrary time delay.According to (1), "this relation holds for any values of t 1 , t 2 , and T, and can thus be applied to the particular case" where T = −t 2 (4) that results in S ¼ Eð0Þ ZZRðt 1 ,t 2 ÞEðt 1 − t 2 Þdt 1 dt 2 ð2ÞExpressing R(t 1 ,t 2 ), E(t) as functions of their Fourier transforms R(w 1 ,w 2 ), E(w) ≡ A(w)e if(w)

Communication: Conditions for one-photon coherent phase control in isolated and open quantum systems

“…2 That proof deals with gas-phase photofragmentation of isolated molecules, with a focus on the long time limit at fixed energy in a degenerate continuum. However, a recent experiment on weak-field shapedpulse cis/trans isomerization of retinal, 3 as well as computational studies on model systems, 4 claims a demonstration of one-photon control of long-time isomerization yields by varying the relative phases of components of the incident radiation. In both cases, the system isomerization takes place within an open dissipative environment, where the earlier proof does not apply.…”

Enhanced Photocurrent in Engineered Bacteriorhodopsin Monolayer

“…4 The retinal isomerization occurs within a few picoseconds of the photocycle initiation and changes the position of the Schiff base by ∼0.4 Å. 11,12 Even though this charge redistribution induces both an internal photovoltage within ns of illumination 13 and a significant change in the spectral properties of BR (λ max changes from 568 to 412 nm), 14 it results in a relatively minor conformational change (concentrated mainly in the orientation of helices F and G). 15 Here, the M163C mutation on the E-F loop of BR has been designed to exploit this sensitivity, that is to bring the most responsive part of the protein into close proximity to the underlying surface.…”

Coherent one-photon phase control in closed and open quantum systems: A general master equation approach

“…A seminal proof 3 showed that one-photon phase control was not possible for isolated molecular systems in which control is over products in the continuum. A subsequent experiment on control of retinal isomerization in bacteriorhodopsin 4 motivated controversy [5][6][7][8] and the need for clarification of conditions under which such control was possible. This clarification, provided in Ref.…”