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A simple and general strategy for generating frequency-anticorrelated photon pairs.

Zhang X, Xu C, Ren Z - Sci Rep (2016)

Bottom Line: To reduce the required flux, a promising solution is to use highly frequency-anticorrelated photon pairs, which are known to induce two-photon transitions much more efficiently.It is shown quantitatively that this strategy can generate highly frequency-anticorrelated photon pairs which can dramatically enhance two-photon excitation efficiency.We believe the proposed strategy can guide new designs for generating frequency-anticorrelated photon pairs.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Key Laboratory of Modern Acoustics, Nanjing University, Nanjing 210008, China.

ABSTRACT
Currently, two-photon excitation microscopy is the method of choice for imaging living cells within thick specimen. A remaining problem for this technique is the damage caused by the high photon flux in the excitation region. To reduce the required flux, a promising solution is to use highly frequency-anticorrelated photon pairs, which are known to induce two-photon transitions much more efficiently. It is still an open question what the best scheme is for generating such photon pairs. Here we propose one simple general strategy for this task. As an example, we show explicitly that this general strategy can be realized faithfully within the widely applicable coherently pumped Jaynes-Cummings model. It is shown quantitatively that this strategy can generate highly frequency-anticorrelated photon pairs which can dramatically enhance two-photon excitation efficiency. We believe the proposed strategy can guide new designs for generating frequency-anticorrelated photon pairs.

No MeSH data available.


Related in: MedlinePlus

Comparison of two-photon excitation induced fluorescence.This figure gives the ratio of the amount of two-photon excitation induced fluorescence achieved by the frequency-anticorrelated photon pair (equation (6))  to the maximum achievable amount by the uncorrelated photon pair (equation (7)) , as a function of the decay constant γe. γe characterizes the rate at which the excited state /e〉 (cf. Fig. 6) decays into the fluorescence photon modes (cf. Methods). Black dashed line: the estimated asymptotic enhancement factor . Red dashed line: the estimated enhancement factor as a function of γe, . Black solid line: exact results (cf. Methods). As can be seen, when the spontaneous decay rate from the final state /e〉 is small, the frequency-anticorrelated photon pair can give a near seventy-fold enhancement in two-photon excitation induced fluorescence for the typical parameter combination studied here. Je = Jm = 10−5, γm = 10−3, δm = 1000 in equations (10) and (11), other parameters are the same as in Fig. 3.
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f7: Comparison of two-photon excitation induced fluorescence.This figure gives the ratio of the amount of two-photon excitation induced fluorescence achieved by the frequency-anticorrelated photon pair (equation (6)) to the maximum achievable amount by the uncorrelated photon pair (equation (7)) , as a function of the decay constant γe. γe characterizes the rate at which the excited state /e〉 (cf. Fig. 6) decays into the fluorescence photon modes (cf. Methods). Black dashed line: the estimated asymptotic enhancement factor . Red dashed line: the estimated enhancement factor as a function of γe, . Black solid line: exact results (cf. Methods). As can be seen, when the spontaneous decay rate from the final state /e〉 is small, the frequency-anticorrelated photon pair can give a near seventy-fold enhancement in two-photon excitation induced fluorescence for the typical parameter combination studied here. Je = Jm = 10−5, γm = 10−3, δm = 1000 in equations (10) and (11), other parameters are the same as in Fig. 3.

Mentions: For the uncorrelated photon pairs, the maximum amount of fluorescence is reached under optimal choices of κu.c. and we denote this to be . To assess whether the frequency-anticorrelated photon pairs can offer some further enhancement, we need to study the ratio of the amount of fluorescence induced by the frequency-anticorrelated photon pairs Fa.c. to the above . In the limit that the width of the final state /e〉 is very small, it is expected that only those components in the wave function with can contribute to two-photon excitation. According to this expectation, the amount of fluorescence should be roughly proportional to . Using this expression a simple calculation then gives , i.e., twice the ratio of the individual photon width to the sum-frequency width. In the cases that the width of the excited state (γe + 2Je) is not negligible, intuitively it can be viewed as a wider sum-frequency width of the incoming photon pair instead of a wider width of the excited state. This gives the estimation for non-negligible (γe + 2Je). Thus it is expected that when the width of the excited state /e〉 is small compared to the sum-frequency width (κ − κ−), the enhancement factor will reach the maximum value of 2κ/(κ − κ−), which can be quite large according to the analysis in the previous subsection. Indeed, as shown in Fig. 7 for the typical parameter combination studied here, when the width of the final state /e〉 is small, the frequency-anticorrelated photon pairs (equation (6)) can give a near seventy-fold enhancement over the maximum achievable amount by uncorrelated photon pairs. Also, it can be seen that the intuitive estimation (red dashed line in Fig. 7) agrees very well with the rigorous result (black solid line in Fig. 7). Practically, this implies that for a two-photon transition with a far-detuned intermediate state, it would be more desirable to use a frequency-anticorrelated photon pair with relatively large absolute widths, so that a same width of the final state /e〉 will appear comparatively narrower and the enhancement factor will be larger.


A simple and general strategy for generating frequency-anticorrelated photon pairs.

Zhang X, Xu C, Ren Z - Sci Rep (2016)

Comparison of two-photon excitation induced fluorescence.This figure gives the ratio of the amount of two-photon excitation induced fluorescence achieved by the frequency-anticorrelated photon pair (equation (6))  to the maximum achievable amount by the uncorrelated photon pair (equation (7)) , as a function of the decay constant γe. γe characterizes the rate at which the excited state /e〉 (cf. Fig. 6) decays into the fluorescence photon modes (cf. Methods). Black dashed line: the estimated asymptotic enhancement factor . Red dashed line: the estimated enhancement factor as a function of γe, . Black solid line: exact results (cf. Methods). As can be seen, when the spontaneous decay rate from the final state /e〉 is small, the frequency-anticorrelated photon pair can give a near seventy-fold enhancement in two-photon excitation induced fluorescence for the typical parameter combination studied here. Je = Jm = 10−5, γm = 10−3, δm = 1000 in equations (10) and (11), other parameters are the same as in Fig. 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834487&req=5

f7: Comparison of two-photon excitation induced fluorescence.This figure gives the ratio of the amount of two-photon excitation induced fluorescence achieved by the frequency-anticorrelated photon pair (equation (6)) to the maximum achievable amount by the uncorrelated photon pair (equation (7)) , as a function of the decay constant γe. γe characterizes the rate at which the excited state /e〉 (cf. Fig. 6) decays into the fluorescence photon modes (cf. Methods). Black dashed line: the estimated asymptotic enhancement factor . Red dashed line: the estimated enhancement factor as a function of γe, . Black solid line: exact results (cf. Methods). As can be seen, when the spontaneous decay rate from the final state /e〉 is small, the frequency-anticorrelated photon pair can give a near seventy-fold enhancement in two-photon excitation induced fluorescence for the typical parameter combination studied here. Je = Jm = 10−5, γm = 10−3, δm = 1000 in equations (10) and (11), other parameters are the same as in Fig. 3.
Mentions: For the uncorrelated photon pairs, the maximum amount of fluorescence is reached under optimal choices of κu.c. and we denote this to be . To assess whether the frequency-anticorrelated photon pairs can offer some further enhancement, we need to study the ratio of the amount of fluorescence induced by the frequency-anticorrelated photon pairs Fa.c. to the above . In the limit that the width of the final state /e〉 is very small, it is expected that only those components in the wave function with can contribute to two-photon excitation. According to this expectation, the amount of fluorescence should be roughly proportional to . Using this expression a simple calculation then gives , i.e., twice the ratio of the individual photon width to the sum-frequency width. In the cases that the width of the excited state (γe + 2Je) is not negligible, intuitively it can be viewed as a wider sum-frequency width of the incoming photon pair instead of a wider width of the excited state. This gives the estimation for non-negligible (γe + 2Je). Thus it is expected that when the width of the excited state /e〉 is small compared to the sum-frequency width (κ − κ−), the enhancement factor will reach the maximum value of 2κ/(κ − κ−), which can be quite large according to the analysis in the previous subsection. Indeed, as shown in Fig. 7 for the typical parameter combination studied here, when the width of the final state /e〉 is small, the frequency-anticorrelated photon pairs (equation (6)) can give a near seventy-fold enhancement over the maximum achievable amount by uncorrelated photon pairs. Also, it can be seen that the intuitive estimation (red dashed line in Fig. 7) agrees very well with the rigorous result (black solid line in Fig. 7). Practically, this implies that for a two-photon transition with a far-detuned intermediate state, it would be more desirable to use a frequency-anticorrelated photon pair with relatively large absolute widths, so that a same width of the final state /e〉 will appear comparatively narrower and the enhancement factor will be larger.

Bottom Line: To reduce the required flux, a promising solution is to use highly frequency-anticorrelated photon pairs, which are known to induce two-photon transitions much more efficiently.It is shown quantitatively that this strategy can generate highly frequency-anticorrelated photon pairs which can dramatically enhance two-photon excitation efficiency.We believe the proposed strategy can guide new designs for generating frequency-anticorrelated photon pairs.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Key Laboratory of Modern Acoustics, Nanjing University, Nanjing 210008, China.

ABSTRACT
Currently, two-photon excitation microscopy is the method of choice for imaging living cells within thick specimen. A remaining problem for this technique is the damage caused by the high photon flux in the excitation region. To reduce the required flux, a promising solution is to use highly frequency-anticorrelated photon pairs, which are known to induce two-photon transitions much more efficiently. It is still an open question what the best scheme is for generating such photon pairs. Here we propose one simple general strategy for this task. As an example, we show explicitly that this general strategy can be realized faithfully within the widely applicable coherently pumped Jaynes-Cummings model. It is shown quantitatively that this strategy can generate highly frequency-anticorrelated photon pairs which can dramatically enhance two-photon excitation efficiency. We believe the proposed strategy can guide new designs for generating frequency-anticorrelated photon pairs.

No MeSH data available.


Related in: MedlinePlus