Open Access Nano Idea

Coherent optical spectroscopy in a biological semiconductor quantum dot-DNA hybrid system

Jin-Jin Li and Ka-Di Zhu*

Author Affiliations

Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China

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Nanoscale Research Letters 2012, 7:133  doi:10.1186/1556-276X-7-133


The electronic version of this article is the complete one and can be found online at: http://www.nanoscalereslett.com/content/7/1/133


Received:24 September 2011
Accepted:16 February 2012
Published:16 February 2012

© 2012 Li and Zhu; licensee Springer.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We theoretically investigate coherent optical spectroscopy of a biological semiconductor quantum dot (QD) coupled to DNA molecules. Coupling with DNAs, the linear optical responses of the peptide QDs will be enhanced significantly in the simultaneous presence of two optical fields. Based on this technique, we propose a scheme to measure the vibrational frequency of DNA and the coupling strength between peptide QD and DNA in all-optical domain. Distinct with metallic quantum dot, biological QD is non-toxic and pollution-free to environment, which will contribute to clinical medicine experiments. This article leads people to know more about the optical behaviors of DNAs-quantum dot system, with the currently popular pump-probe technique.

1 Introduction

Rapid and highly sensitive detection of DNA molecules contributes to ultrasensitive and automated biological assays such as sensing, imaging, immunoassay, and other diagnostics applications [1-3]. Conventional approaches have focused on inorganic/organic hybrid DNA biomedicine sensors for biological labels, cell tracking, and monitoring response to therapeutic agents [4-6]. Among numerical hybrid components, the unique size-dependent, narrow, symmetric, bright, and stable fluorescence of quantum dots (QDs) have made themselves powerful tools for investigating a wide range of biological problems [7]. This is a difficult task with standard fluorophores because their relatively narrow excitation and broad emission spectra often result in spectra overlap. Besides, the optical behaviors of quantum dots are typically unaffected while they are conjugating to bio-molecules, which make them highly stable and bright probes, especially suitable for photon-limited in vivo studies and continuous tracking experiments over extended time periods [7]. Recently, the coherent optical spectroscopy of a strongly driven quantum dot has been experimentally investigated by Xu et al. [8,9]. They have shown that, like single atom two- and three-level quantum systems, single QD can also exhibit interference phenomena including Autler-Townes splitting and gain without population inversion when driven simultaneously by two optical fields. In this case, researchers are indulged in quantum dots and DNA conjugates to study biological activities and medical diagnosis [10,11], which have applications in biomolecule targets exploitation [12,13]. But for the research of coherent optical spectrum in such coupled DNAs-QD, no study has ever been undertaken, neither in experiment nor in theory.

Furthermore, there is another question. The metallic quantum dots used in biological assays always have toxicity, which may limit the capabilities of biomedicine assays and bring in some unnecessary troubles. So the search for cadmium-free quantum dots has therefore becomes another major research area. Most recently, Amdursky et al. [14,15] have experimentally demonstrated that the peptide quantum dots represent one of the simplest forms of quantum dot and the most important feature of these quantum dots is the nontoxicity to the environment and to human body. These quantum dots will become new labeling materials in biological and biomedical assays. However, the coherent optical properties of such QDs coupled to DNAs are still lacking.

In the present study, we theoretically investigate the coherent optical spectroscopy for a peptide quantum dot (QD) coupled to DNA molecules, with pump-probe technique. Recently, this two-laser technique has been realized by several groups [16-20] while investigating the optomechanical system. Here we show that this hybrid peptide QD-DNA system will become transparent due to the DNA's vibrations when applying a strong control laser. Under some conditions the output signal laser even be enhanced significantly. Furthermore, the vibrational frequency of DNA molecule and the coupling strength between peptide QD and DNA can be measured due to the absorption splitting peaks in all-optical domain.

2 Model and theory

We consider a system composed of a biological semiconductor neutral quantum dot and DNA molecules in the simultaneous presence of a strong control field and a weak signal field. The physical situation is illustrated in Figure 1a. Figure 1b shows the energy levels of peptide QD when dressing the vibrational modes of DNA molecules. The energy levels of peptide quantum dot can be modeled as traditional quantum dot, which consists of two energy states, the ground state |g〉 and the first excited state (single exciton) |ex〉. Usually, this two-level exciton can be characterized by the pseudospin -1/2, operators S± and Sz. The coherent optical spectroscopy of a strongly driven quantum dot without DNA molecules has been experimentally investigated by Xu et al. [8,9]. Then the Hamiltonian of exciton in a QD can be described by

thumbnailFigure 1. Schematic diagram of a peptide quantum dot coupled to DNA molecules. (a) A single peptide QD coupled to DNA molecules in the simultaneous presence of two optical fields. (b) The energy levels of QD when dressing the vibrational modes of DNA molecules.

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M1">View MathML</a>

(1)

where ωex is the exciton frequency of peptide quantum dot.

We use the following Hamiltonian to describe DNA molecules, which is modeled as a harmonic oscillator and described by the position and momentum operators q and p, which have a commutation relation [q, p] = iħ [21], and then

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M2">View MathML</a>

(2)

where mi and ωi are the mass and vibrational frequency of DNA molecule, respectively.

In the unlimited or large volume of aqueous solution, all the vibrational modes of DNA molecules are strongly attenuated. But in a small volume of aqueous solution, the DNA longitudinal vibrational modes decayed slowly, while the other vibrational modes remain strong attenuation [22]. Therefore, for small volume aqueous solution of DNA molecules coupled to a quantum dot system, only the longitudinal modes of DNA molecules can be taken into account. Such vibrational mode of DNA can be simulated as harmonic vibration of spring oscillator. Since the flexion of DNA molecules induces extensions and compressions in the structure of Figure 1a, the longitudinal strain will modify the energy of the electronic states of QD through deformation potential coupling [23,24]. Then the Hamiltonian of the vibrational modes of DNA molecules coupled to the peptide QD can be described by

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M3">View MathML</a>

(3)

where Mi is the coupling strength between the peptide QD and the ith DNA. It is should be noted that due to the dilute aqueous solution of DNA molecules, here we do not consider the effect of the coupling between the DNA molecules although it may be significant in the dense aqueous solutions [22].

The Hamiltonian of the peptide quantum dot coupled to the strong control field and weak signal field is described as

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M4">View MathML</a>

(4)

where μ is the electric dipole moment of the exciton, ωc (ωs) is the frequency of the control field (signal field), and Ec (Es) is the slowly varying envelope of the control field (signal field). Therefore, we obtain the total Hamiltonian of the coupled peptide QD-DNA in the presence of two optical fields as follows

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M5">View MathML</a>

(5)

In a rotating frame at the control field ωc, the total Hamiltonian of the system reads as

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M6">View MathML</a>

(6)

where Δc = ωex - ωc, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M7">View MathML</a>, Ωc is the Rabi frequency of the control field, and δ = ωs - ωc is the detuning between the signal field and the control field.

Furthermore, we may consider the decoherence and relaxation of exciton and DNA mode in combination with their interaction to external environments into the Hamiltonian [25-28]. In general, the environments can be described as independent ensembles of harmonic oscillators with spectral densities. We also assume that DNA molecules interact bilinearly with external environment via its position, and the exciton interacts with the environment through Sx operator and Sz operator. The Sx coupling to the environment models the relaxation process of the exciton, while the Sz coupling to the environment models the pure dephasing process of the exciton [25-28]. On the other hand, because ωex is much larger than ωi, it is reasonable to use the rotating-wave approximation to the exciton-environment coupling term, but not to the DNA-environment coupling term in the system-environment coupling Hamiltonian.

In accordance with standard procedure [25-28], we can obtain the Born-Markovian master equation of the reduced density matrix of the coupled system, ρ (t), through tracing out the environmental degrees of freedom as

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M8">View MathML</a>

(7)

where the coefficients A, B, E, D, G, and L correspond to the characteristics of the coupling, and to the structure and properties of the environments. Their explicit form can be written as <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M9">View MathML</a>, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M10">View MathML</a>, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M11">View MathML</a>, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M12">View MathML</a>, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M13','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M13">View MathML</a>, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M14','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M14">View MathML</a>, where γ1 = 2π Jx ( ωex), γ2 = 2π Jz(0), γ3 = 2π Jc(ωi) <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M15','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M15">View MathML</a>. <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M16','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M16">View MathML</a> is the Boltzman-Einstein distribution of the thermal equilibrium environments. Jx, Jz, and Jc describe the spectral densities of the respective environments coupled through Sx and Sz to the exciton, and through Q to the DNA molecule, respectively. <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M17','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M17">View MathML</a> denotes the principal value of the argument.

According to the master equation (7), we can obtain the equation of motion for the expectation value of any physical operator O of the coupled system by calculating <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M18','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M18">View MathML</a>. We thus have

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M19','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M19">View MathML</a>

(8)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M20','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M20">View MathML</a>

(9)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M21','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M21">View MathML</a>

(10)

where <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M22','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M22">View MathML</a> corresponds to the peptide QD-DNA coupling strength, ωD is the DNA longitudinal vibrational modes, Γ1 and Γ2 are the exciton relaxation rate and dephasing rate, respectively, τD is the vibrational lifetime of DNA molecule [29]. They are derived microscopically as

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M23','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M23">View MathML</a>

(11)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M24','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M24">View MathML</a>

(12)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M25','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M25">View MathML</a>

(13)

Note that if the pure dephasing coupling is neglected, i.e., γ2 = 0, then Γ1 = 2Γ2. In order to solve these equations, we first take the semiclassical approach by factorizing the DNA molecule and exciton degrees of freedom, i.e., 〈QSz〉 = 〈Q〉〈Sz〉, in which any entanglement between these systems should be ignored. And then we make the following ansatz [30]

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M26','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M26">View MathML</a>

(14)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M27','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M27">View MathML</a>

(15)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M28','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M28">View MathML</a>

(16)

Upon substituting these equations to Equations (8)-(10) and working to the lowest order in Es, but to all orders in Ec, we finally obtain the linear optical susceptibility S+ in the steady state as the following solution

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M29','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M29">View MathML</a>

(17)

where the dimensionless susceptibility χ(ωs) is given by

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M30','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M30">View MathML</a>

(18)

where the function f(δ0) and auxiliary function η(ωs) are given by

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M31','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M31">View MathML</a>

(19)

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M32','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M32">View MathML</a>

(20)

where e1 = i + Δc00/(2w0), e2 = ic0 + λ0/(2w0), δ0 = δ2, Ωc0 = Ωc2, λ0 = λ/Γ2 ωD0 = ωD2, τD0 = τDΓ2, Δc0 = Δc2, <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M33','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M33">View MathML</a>, and Γ1 = 2Γ2.

And the population inversion (w0) of the exciton is determined by the following equation

<a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M34','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M34">View MathML</a>

(21)

3 Results and discussions

For illustration of the numerical results, we choose the realistic coupled system of a peptide QD linked to the DNA molecules in the simultaneous presence of a strong control beam and a weak signal beam as shown in Figure 1. In such coupled system, many DNA molecules linked with one QD. These DNA molecules in solution form may be distorted in mess, but one can extend these molecules into linear form by applying electromagnetic field or fluid force [31]. In addition, the longitudinal vibrational frequency can be determined by the length of DNA molecules. In the theoretical calculation, we select the vibrational frequency and the lifetime of DNA molecule are ωD = 32 GHz and τD = 3 ns, respectively [24,32-34]. The decay time of peptide quantum dot is 6 fs [15], which corresponds to Γ1 = 160 THz.

Figure 2a shows the signal absorption spectrum as a function of control-signal detuning. In the middle of the figure, we can see that the features appear in the signal absorption spectrum as those in atomic two-level systems [30]. However, the new features which are different from those in atomic systems without DNA molecules also appear at the both sides of the spectrum. Figure 2b gives the origin of these new features. The leftmost (1) of Figure 2b shows the dressed states of exciton when coupling with DNA molecules (|n〉 denotes the number states of the DNA molecules). Part (2) shows the origin of DNA vibrational mode induced three-photon resonance. Here the electron makes a transition from the lowest dressed level |g, n〉 to the highest dressed level |ex, n + 1〉 by the simultaneous absorption of two control photons and emission of a photon at ωc - ωD. This process can amplify a wave at δ = -ωD, as indicated by the region of negative absorption in Figure 2a. The part (3) in Figure 2b shows the origin of DNA stimulated Rayleigh resonance. The Rayleigh resonance corresponds to a transition from the lowest dressed level |g, n〉 to the dressed level |ex, n〉. Each of these transitions is centered on the frequency of the control laser. The rightmost part (4) corresponds to the usual absorption resonance as modified by the ac Stark effect.

thumbnailFigure 2. The absorption spectrum of signal laser and the energy levels of exciton when a single peptide QD coupling with the vibration of DNA molecules. (a) The absorption spectrum of signal laser in the presence of two optical fields for the case <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M35','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M35">View MathML</a>, Δc0 = 0, λ0 = 0.5, ωD0 = 4, τD0 = 33. (b) The energy levels of exciton when coupling with the vibration of DNA molecules. Part (2), (3), and (4) correspond to the transitions of the left peak, center feature and right peak, respectively, shown in (a).

3.1 Vibrational frequency measurement of DNA molecule

We first fix the control-exciton detuning Δc = 0, and scan the signal laser across the exciton frequency the signal spectrum shown in Figure 3 provides us a simple method to detect the frequency of DNA molecule. The two steep peaks shown in the both sides of the spectrum corresponds the vibrational frequency of DNA molecule. For example, if the frequency of DNA is 32 GHz, the two steep peaks will be located at ±32 GHz (the top curve of Figure 3). The location of two peaks can be changed with different frequencies of DNA molecules (the other two plots in Figure 3). In this case, this control-signal technique offered a simple and effective method for the detection of DNA vibrational frequency. We note that the left peak is a negative absorption, which means the output signal light can be amplified in this region. Using the gain region, we may use the peptide QD as a label to discriminate the biological molecules by applying two optical lasers. For more specific description of DNA enhanced spectrum, we further investigate the signal transmission spectrum as a function of the control laser intensity as shown in Figure 4. The amplification of signal laser increases with increasing of control laser intensity as shown in the inset of Figure 4.

thumbnailFigure 3. The absorption spectrum of signal laser with different frequencies of DNA molecule. The parameters used are Ic = 1.7W/cm2, Δc = 0, λ = 0.8 GHz, τD = 3 ns.

thumbnailFigure 4. The characteristic curve of peptide QD-DNA system by plotting the transmission of the signal laser as a function of the control laser intensity. The other parameters used are Ic = 1.7W/cm2, Δc = -32 GHz, λ = 0.8 GHz, ωD = 32 GHz, τD = 3 ns.

3.2 Coupling strength determination between peptide quantum dot and DNA molecule

Next, the coupling strength between peptide quantum dot and DNA molecule can be measured using the pump-probe technique. The absorption spectrum will spit into two peaks and have a zero absorption at Δs = 0, if we fix the control laser detuning on the vibrational frequency of DNA molecule (Δc = ωD). Figure 5 exhibits that the coupling strength can be measured by the distance of peak splitting in the signal absorption spectrum. However, in the absence of the coupling between peptide quantum dot and DNA molecule, the splitting peaks disappear quickly and turn to a totally absorption peak (see the solid line). This is due to DNA vibration induced coherent population oscillation which makes a deep hole at Δs = 0 in the signal absorption spectrum as δ = ωD. The inset of Figure 5 shows the linear relationship between the peak splitting and the coupling strength of peptide QD-DNA, which provides us an effective method to detect the coupling strength between QD and DNA. This peak splitting is very similar to the Rabi splitting of two-level systems in quantum optics [35].

thumbnailFigure 5. The absorption spectrum of signal laser as a function of the detuning between signal laser and exciton for four difference coupling of peptide QD-DNA. The parameters used are <a onClick="popup('http://www.nanoscalereslett.com/content/7/1/133/mathml/M35','MathML',630,470);return false;" target="_blank" href="http://www.nanoscalereslett.com/content/7/1/133/mathml/M35">View MathML</a>, Δc0 = 4, ωD0 = 4, tD0 = 33.

Furthermore, in conventional QD-linked biomedicine sensors, excited by single optical field, the fluorescence emission efficiencies still remain challenge due to the coated chemicals, the autofluorescence of background and the copy number of the target to each QD [36]. However, the emission efficiency would be largely enhanced in coherent optical driven by double optical fields, described in this article. From Figure 4, we find that the amplified signal field comes from the quantum interference between the hybrid components and external lasers, which has no relevant with spontaneous fluorescence lifetime of quantum dot. In this case, we anticipate that DNA-linked peptide QD system excited by control-signal technique can be applied to biological imaging, which are nontoxic to environment and human body. For example, once the peptide quantum dot is attached to abnormal DNA molecules, we first apply a strong control field to the peptide QD, provided by Δc = -ωD, then the hybrid system is transparent to other optical fields. Thereafter, we apply a second weak signal beam across the exciton frequency, then the output signal beam can be amplified at Δs = 0, which means the peptide quantum dot can be luminant in all-optical domain. Meanwhile, different vibrational frequencies of DNA molecule and the coupling strengths between quantum dot and DNA result in different amplitudes of amplification, which are shown in Figures 4 and 5. This is the DNA enhanced signal spectroscopy of peptide quantum dot, which will have a potential applications in cellular imaging, immunoassays, and clinical diagnosis.

4 Conclusions

In this article, we theoretically investigated the coherent optical spectroscopy in a coupled DNA-peptide quantum dot system in the presence of two optical fields. Theoretical analysis shows that the vibrational frequency of DNA and the coupling strength between peptide QD and DNA can be measured effectively and precisely in all-optical domain. Finally, we hope that our predictions in the present study can be testified by experiments in the near future.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

JJL finished the main work of this article, including deducing the formulas, plotting the figures, and drafting the manuscript. KDZ conceived of the idea, participated in its writing and provided some useful suggestions. All authors read and approved the final manuscript.

Acknowledgements

The part of this study was supported by the National Natural Science Foundation of China (Nos. 10774101 and 10974133).

References

  1. Kuzuya A, Sakai Y, Yamazaki T, Xu Y, Komiyama M: Nanomechanical DNA origami 'single-molecule beacons' directly imaged by atomic force microscopy.

    Nat Commun 2011, 2:449. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  2. Finkelstein IJ, Visnapuu ML, Greene EC: Single-molecule imaging reveals mechanisms of protein disruption by a DNA translocase.

    Nat Commun 2010, 468:983. OpenURL

  3. Boukany PE, Hemminger O, Wang SQ, Lee LJ: Molecular imaging of slip in entangled DNA solution.

    Phys Rev Lett 2010, 105:027802. PubMed Abstract | Publisher Full Text OpenURL

  4. Kamiya K, Okada S: Energetics and electronic structure of encapsulated single-stranded DNA in carbon nanotubes.

    Phys Rev B 2011, 83:155444. OpenURL

  5. Cherepinsky V, Hashmi G, Mishra B: Competitive hybridization models.

    Phys Rev E 2010, 82:051914. OpenURL

  6. Tikhomirov G, Hoogland S, Lee PE, Fischer A, Sargent EH, Kelley SO: DNA-based programming of quantum dot valency, self-assembly and luminescence.

    Nat Nanotechnol 2011, 6:485. PubMed Abstract | Publisher Full Text OpenURL

  7. Fu A, Gu WW, Larabell C, Alivisatos AP: Semiconductor nanocrystals for biological imaging.

    Curr Opin Neurobiol 2005, 15:568. PubMed Abstract | Publisher Full Text OpenURL

  8. Xu XD, Sun B, Berman PR, Steel DG, Bracker AS, Gammon D, Sham LJ: Coherence optical spectroscopy of a strongly driven quantum dot.

    Science 2007, 317:929. PubMed Abstract | Publisher Full Text OpenURL

  9. Xu XD, Sun B, Kim ED, Smirl K, Berman PR, Steel DG, Bracker AS, Gammon D, Sham LJ: Single charged quantum dot in a strong optical field: absorption, gain, and the ac-Stark effect.

    Phys Rev Lett 2008, 101:227401. PubMed Abstract | Publisher Full Text OpenURL

  10. Medintz IL, Uyeda HT, Goldman ER, Mattoussi H: Quantum dot bio-conjugates for imaging labelling and sensing.

    Nat Mater 2005, 4:435. PubMed Abstract | Publisher Full Text OpenURL

  11. Medintz IL, Clapp AR, Mattoussi H, Goldman ER, Fisher B, Mauro JM: Self-assembled nanoscale biosensors based on quantum dot FRET donors.

    Nat Mater 2003, 2:630. PubMed Abstract | Publisher Full Text OpenURL

  12. Gao XH, Cui YY, Levenson RM, Chung LWK, Nie S: In vivo cancer targeting and imaging with semiconductor quantum dots.

    Nat Biotech-nol 2004, 22:969. OpenURL

  13. Cai WB, Chen XY: Preparation of peptide-conjugated quantum dots for tumor vasculature-targeted imaging.

    Nat Protocol 2008, 3:89. Publisher Full Text OpenURL

  14. Amdursky N, Molotskii M, Gazit E, Rosenman G: Self-assembled bioin-spired quantum dots: optical properties.

    Appl Phys Lett 2009, 94:261907. Publisher Full Text OpenURL

  15. Amdursky N, Molotskii M, Gazit E, Rosenman G: Elementary building blocks of self-assembled peptide nanotubes.

    J Am Chem Soc 2010, 132:15632. PubMed Abstract | Publisher Full Text OpenURL

  16. Weis S, Rivièere R, Deléeglise S, Gavartin E, Arcizet O, Schliesser A, Kip-perberg TJ: Optomechanically induced transparency.

    Science 2010, 330:1520. PubMed Abstract | Publisher Full Text OpenURL

  17. Teufel JD, Li D, Allman MS, Cicak K, Sirois AJ, Whittaker JD, Simmonds RW: Circuit cavity electromechanics in the strong-coupling regime.

    Nature 2011, 471:204. PubMed Abstract | Publisher Full Text OpenURL

  18. Safavi-Naeini AH, Mayer Alegre TP, Chan J, Eichenfield M, Winger M, Lin Q, Hill JT, Chang DE, Painter O: Electromagnetically induced transparency and slow light with optomechanics.

    Nature 2011, 472:69. PubMed Abstract | Publisher Full Text OpenURL

  19. Li JJ, Zhu KD: A scheme for measuring vibrational frequency and coupling strength in a coupled annomechancial resonator-quantum dto system.

    Appl Phys Lett 2009, 94:063116.

    94:249903

    Publisher Full Text OpenURL

  20. He W, Li JJ, Zhu KD: Coupling-rate determination based on radiation-pressure-inducd normal mode splitting in cavity optomechanical systems.

    Opt Lett 2010, 35:339. PubMed Abstract | Publisher Full Text OpenURL

  21. Van Zandt LL: Resonant microwave absorption by dissolved DNA.

    Phys Rev Lett 1986, 57:2085. PubMed Abstract | Publisher Full Text OpenURL

  22. Dorfman BH: The effects of viscous water on the normal mode vibrations of DNA.

    Dissert Abstr Int 1984, 45:2213. OpenURL

  23. Edwards GS, Davis CC, Saffer JD, Swicord ML: Resonant microwave absorption of selected DNA molecules.

    Phys Rev Lett 1984, 53:1284. Publisher Full Text OpenURL

  24. Edwards GS, Davis CC, Saffer JD, Swicord ML: Microwave-field-driven acoustic modes in DNA.

    Biophys J 1985, 47:799. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  25. Gardiner CW, Zoller P: Quantum Noise. 2nd edition. Berlin: Springer; 2000:425. OpenURL

  26. Walls DF, Milburn GJ: Quantum Optics. Berlin: Springer; 1994:245. OpenURL

  27. Carmichael H: Statistical Methods in Quantum Optics I. Berlin: Springer; 1999:261. OpenURL

  28. Breuer HP, Petruccione F: The Theory of Open Quantum Systems. Oxford: Oxford University Press; 2002:441. OpenURL

  29. de M Donega C, Bode M, Meijerink A: Size-and temperature-dependence of exciton lifetimes in CdSe quantum dots.

    Phys Rev B 2006, 74:085320. OpenURL

  30. Boyd RW: Nonlinear Optics. Amsterdam: Academic Press; 2008:313. OpenURL

  31. Marko JF, Siggia ED: Stretching DNA.

    Macromolecules 1995, 28:8759. Publisher Full Text OpenURL

  32. Yuan CL, Chen HM, Lou XW, Archer LA: DNA bending stiffness on small length scales.

    Phys Rev Lett 2008, 100:018102. PubMed Abstract | Publisher Full Text OpenURL

  33. Gill R, Willner I, Shweky I, Banin U: Fluorescence resonance energy transfer in CdSe/ZnS-DNA conjugates: probing hybridization and DNA cleavage.

    J Phy Chem B 2005, 109:23715. Publisher Full Text OpenURL

  34. Adair BK: Vibrational resonances in biological systems at microwave.

    Biophys J 2002, 82:1147. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  35. Khitrova G, Gibbs HM, Kira M, Koch SW, Scherer A: Vacuum Rabi splitting in semiconductors.

    Nat Phys 2006, 2:81. Publisher Full Text OpenURL

  36. Zhou DJ, Ying LM, Hong X, Hall EA, Abell C, Klenerman D: A compact functional quantum dot-DNA conjugate: preparation, hybridization, and specific label-free DNA detection.

    Langmuir 2008, 24:1659. PubMed Abstract | Publisher Full Text OpenURL