Coherent optical spectroscopy in a biological semiconductor quantum dot-DNA hybrid system
© Li and Zhu; licensee Springer. 2012
Received: 24 September 2011
Accepted: 16 February 2012
Published: 16 February 2012
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.
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 . 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 . 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
where ω ex is the exciton frequency of peptide quantum dot.
where m i and ω i are the mass and vibrational frequency of DNA molecule, respectively.
where M i is the coupling strength between the peptide QD and the i th 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 .
where Δ c = ω ex - ω c , , Ω c is the Rabi frequency of the control field, and δ = ω s - ω c 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 S x operator and S z operator. The S x coupling to the environment models the relaxation process of the exciton, while the S z coupling to the environment models the pure dephasing process of the exciton [25–28]. On the other hand, because ω ex is much larger than ω i , 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.
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 , , , , , , where γ1 = 2π J x ( ω ex ), γ2 = 2π J z (0), γ3 = 2 π J c (ω i ) . is the Boltzman-Einstein distribution of the thermal equilibrium environments. J x , J z , and J c describe the spectral densities of the respective environments coupled through S x and S z to the exciton, and through Q to the DNA molecule, respectively. denotes the principal value of the argument.
where e1 = i + Δc 0-λ0/(2w0), e2 = i-Δc 0+ λ0/(2w0), δ0 = δ/Γ2, Ωc 0= Ω c /Γ2, λ0 = λ/Γ2 ωD 0= ω D /Γ2, τD 0= τ D Γ2, Δc 0= Δ c /Γ2, , and Γ1 = 2Γ2.
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 . 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 ω D = 32 GHz and τ D = 3 ns, respectively [24, 32–34]. The decay time of peptide quantum dot is 6 fs , which corresponds to Γ1 = 160 THz.
3.1 Vibrational frequency measurement of DNA molecule
3.2 Coupling strength determination between peptide quantum dot and DNA molecule
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 . 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 Δ c = -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 Δ s = 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.
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.
The part of this study was supported by the National Natural Science Foundation of China (Nos. 10774101 and 10974133).
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