OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 10 — Nov. 8, 2013
« Show journal navigation

Nanoscale resolution for fluorescence microscopy via adiabatic passage

Juan Luis Rubio, Daniel Viscor, Veronica Ahufinger, and Jordi Mompart  »View Author Affiliations


Optics Express, Vol. 21, Issue 19, pp. 22139-22144 (2013)
http://dx.doi.org/10.1364/OE.21.022139


View Full Text Article

Acrobat PDF (1004 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose the use of the subwavelength localization via adiabatic passage technique for fluorescence microscopy with nanoscale resolution in the far field. This technique uses a Λ-type medium coherently coupled to two laser pulses: the pump, with a node in its spatial profile, and the Stokes. The population of the Λ system is adiabatically transferred from one ground state to the other except at the node position, yielding a narrow population peak. This coherent localization allows fluorescence imaging with nanometer lateral resolution. We derive an analytical expression to asses the resolution and perform a comparison with the coherent population trapping and the stimulated-emission-depletion techniques.

© 2013 OSA

1. Introduction

In the last decades, far-field fluorescence microscopy has experienced great advances with applications in medicine and biology, among other fields, offering the possibility to obtain high resolution images in a non-invasive manner. In lens-based light microscopes, the image of a point object obtained from the fluorescence emitted by a fluorophore placed in the sample is, in principle, limited by diffraction [1

1. E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. 9, 413 (1873). [CrossRef]

]. This image becomes a finite-size spot in the focal plane, mathematically described by the point-spread function (PSF), whose full width at half maximum (FWHM) is λ/(2NA), being λ the wavelength of the addressing light, and NA the numerical aperture of the objective. Due to the reduced dimensions of the samples to investigate, frequently around few nanometers, high resolution images overcoming the diffraction limit are necessary. To this aim, one of the most extended group of techniques is based on the general concept of reversible saturable optical fluorescence transition (RESOLFT) [2

2. S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21, 1347 (2003). [CrossRef] [PubMed]

] between two distinguishable molecular states, such as stimulated-emission-depletion (STED) [3

3. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780 (1994). [CrossRef] [PubMed]

] and ground-state-depletion (GSD) [4

4. S. W. Hell and M. Kroug, “Ground-state-depletion fluorscence microscopy: a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60, 495 (1995). [CrossRef]

]. RESOLFT exploits the spatial inhibition of the fluorescence signal from a light-excited fluorophore in order to engineer the effective PSF, reducing its FWHM.

Parallely, in recent years, there has been an intense activity in the spatial localization of atomic population in Λ-type systems coherently interacting with two electromagnetic fields (see e.g., [5

5. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B: At. Mol. Opt. Phys. 39, 3437 (2006). [CrossRef]

, 6

6. A. V. Gorshkov, L. Jiang, M. Greiner, P. Zoller, and M. D. Lukin, “Coherent quantum optical control with subwavelength resolution,” Phys. Rev. Lett. 100, 093005 (2008). [CrossRef] [PubMed]

]). All these methods are based on the so-called coherent population trapping (CPT) technique or close variations, and have also been considered for microscopy [7

7. D. D. Yavuz and N. A. Proite, “Nanoscale resolution fluorescence microscopy using electromagnetically induced transparency,” Phys. Rev. A 76, 041802(R) (2007). [CrossRef]

, 8

8. K. T. Kapale and S. Agarwal, “Subnanoscale resolution for microscopy via coherent population trapping,” Op. Lett. 35, 2792 (2010). [CrossRef]

, 9

9. H. Li, V. A. Sautenkov, M. M. Kash, A. V. Sokolov, G. R. Welch, Y. V. Rostovtsev, M. S. Zubairy, and M. O. Scully, “Optical imaging beyond the diffraction limit via dark states,” Phys. Rev. A 78, 013803 (2008). [CrossRef]

]). In the context of atomic population localization, some of us have recently proposed the subwavelength localization via adiabatic passage (SLAP) technique [10

10. J. Mompart, V. Ahufinger, and G. Birkl, “Coherent patterning of matter waves with subwavelength localization,” Phys. Rev. A 79, 053638 (2009). [CrossRef]

]. In SLAP, position-dependent stimulated Raman adiabatic passage (STIRAP) [11

11. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998). [CrossRef]

] is performed using spatially dependent fields. This approach provides population peaks narrower than using other coherent localization techniques [5

5. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B: At. Mol. Opt. Phys. 39, 3437 (2006). [CrossRef]

, 7

7. D. D. Yavuz and N. A. Proite, “Nanoscale resolution fluorescence microscopy using electromagnetically induced transparency,” Phys. Rev. A 76, 041802(R) (2007). [CrossRef]

] and its application in nanolitography and patterning of BEC’s [10

10. J. Mompart, V. Ahufinger, and G. Birkl, “Coherent patterning of matter waves with subwavelength localization,” Phys. Rev. A 79, 053638 (2009). [CrossRef]

], and single-site addressing of ultracold atoms [12

12. D. Viscor, J. L. Rubio, G. Birkl, J. Mompart, and V. Ahufinger, “Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage,” Phys. Rev. A 86, 063409 (2012). [CrossRef]

], has already been discussed.

In this work, we propose a SLAP-based nanoscale resolution technique for fluorescence microscopy. At variance with respect to [10

10. J. Mompart, V. Ahufinger, and G. Birkl, “Coherent patterning of matter waves with subwavelength localization,” Phys. Rev. A 79, 053638 (2009). [CrossRef]

, 12

12. D. Viscor, J. L. Rubio, G. Birkl, J. Mompart, and V. Ahufinger, “Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage,” Phys. Rev. A 86, 063409 (2012). [CrossRef]

], two driving laser pulses are applied here to a continuous distribution of emitters, and and we take into account the effect of the objective lens in our model. In section 2, we describe the physical system under consideration, derive an expression for the resolution, and compare it with the one obtained for the CPT case. In section 3, we show numerical results of the SLAP proposal and compare it with the STED technique. Finally, we present the conclusions and point out a possible implementation of the proposed technique using quantum dots.

2. Model

We consider a Λ scheme, where the population is initially in |1〉, see top of Fig. 1(a). Two laser pulses, Stokes (S) and pump (P), couple to transitions |3〉↔|2〉 and |1〉↔|2〉 with Rabi frequencies ΩS(x, t) ≡ μ32 · ES(x, t)/ħ and ΩP(x, t) ≡ μ12 · EP(x, t)/ħ, respectively, where ES (EP) is the electric field amplitude of the Stokes (pump), μ32 (μ12) is the electric dipole moment of the |3〉↔|2〉 (|1〉↔|2〉) transition, and ħ is the reduced Planck constant. The excited level |2〉 has a decay rate γ21 (γ23) to the ground state |1〉 (|3〉). If the two-photon resonance condition is fulfilled, one of the eigenstates of the Hamiltonian, the so-called dark-state, takes the form:
|D(x,t)=[ΩS*(x,t)|1ΩP*(x,t)|3]/Ω(x,t),
(1)
where Ω(x, t) = (|ΩP(x, t)|2 + |ΩS(x, t)|2)1/2. Note that |D(x, t)〉 does not involve the excited state |2〉. In our scheme, and in order to adiabatically follow the dark state, both pulses are sent in a counterintuitive temporal sequence, applying first the Stokes and, with a temporal delay T, the pump [see bottom of Fig. 1(a)]. In addition, to ensure no coupling between the different energy eigenstates, a global adiabatic condition must be fulfilled, which imposes Ω(x)TA, where A is a dimensionless constant that for optimal Gaussian profiles and delay times takes values around 10 [11

11. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998). [CrossRef]

]. In the SLAP technique, the pump pulse has a central node in its spatial profile such that the described temporal sequence of the pulses produces an adiabatic population transfer from |1〉 to |3〉, except at the position of the pump node. Therefore, we obtain a narrow peak of population remaining in |1〉, whose profile can be considered as the PSF function referred to an image object in a lens-based microscope. Note that the FWHM of the population peak determines the resolution of the technique. Finally, an exciting E pulse is used to pump the population remaining in |1〉 either to state |2〉 or to an auxiliary excited state, allowing for the subsequent registration of the fluorescence. If state |2〉 decays radiatively, the pump (P) could be used also as the exciting (E) pulse, reducing the experimental requirements. Figure 1(b) shows a possible setup for the proposal. Right to left, the Stokes, pump and exciting pulses are sent, and we assume that due to the Stokes’s shift, the fluorescence (left arrow) can be separated from the light of the different pulses by, e.g., dichroic mirrors (DM).

Fig. 1: (a) SLAP technique. Top: Λ-system with pump (P) and Stokes (S) pulses coupling the |1〉↔|2〉 and |3〉↔|2〉 transitions, respectively. The decay rate from |2〉 to |1〉 (|3〉) is γ21 (γ23). Bottom: Pulse temporal sequence, being E the exciting pulse. (b) Schematic setup of the SLAP-based fluorescence microscopy. Note the central node of the pump pulse. DM accounts for dichroic mirrors.

To take into account the effect of the objective lens in our model, we consider the Rabi frequency of the Stokes pulse having a Bessel beam spatial profile, and the one of the pump being the result of superimposing two Bessel beams focused with a lateral offset, producing a node in its center. The spatio-temporal profiles of the Stokes and pump fields read:
ΩS(υ,t)=ΩS0F(υ,0)e(ttS)2/σ2,
(2)
ΩP(υ,t)=ΩP0[F(υ,δ)+F(υ,δ)]e(ttP)2/σ2,
(3)
where ΩS0P0) is the peak Rabi frequency of the Stokes (pump) pulse, F(υ,r)2J1(υ+r)υ+r, where J1(υ) is the first order Bessel function and υ = (2πxNA)/λ is the optical unit corresponding to the Cartesian coordinate x in the focal plane, σ is the temporal width of the pulses, T = tPtS is the temporal delay between the pulses, which is proporcional to σ, and δ = 1.22π is the offset with respect to υ = 0 corresponding to the first cutoff of F(υ, 0). It is possible to obtain an analytical expression for the FWHM of the final population peak in |1〉, p1(x), by considering that the global adiabaticity condition is reached for |υ| ≈ FWHM, assuming a Gaussian population peak profile and considering |υ| ≪ δ. Thus, from the spatial profiles in Eqs. (2)(3), the FWHM of the population distribution is
FWHMSLAP=λ2NAδπ(4Rk21+1)1/2,
(4)
where R ≡ (ΩP0S0)2 is the intensity ratio between the pump and the Stokes pulses, and k ≡ ΩS0T/A must fulfill 0 < k < 1. In such a SLAP-based fluorescence microscope, the effective PSF is given by the product hexc(υ) p1(υ) normalized to 1, where hexc(υ) is the PSF of the E pulse. If we assume that all the localized population leads to fluorescence, the lateral resolution is determined by Eq. (4), where the first factor accounts for diffraction, the second one is 1.22, and the third one can be less than 1 depending on the adiabaticity of the process, and tends to zero in the limit R → ∞, i.e., when ΩP0 ≫ ΩS0. Other dark-state techniques proposed to obtain atomic localization [5

5. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B: At. Mol. Opt. Phys. 39, 3437 (2006). [CrossRef]

, 7

7. D. D. Yavuz and N. A. Proite, “Nanoscale resolution fluorescence microscopy using electromagnetically induced transparency,” Phys. Rev. A 76, 041802(R) (2007). [CrossRef]

] are based on the so-called coherent population trapping (CPT) or close variations, in which the fields can be either two continuos waves or two perfectly overlapping long pulses. In this case, to obtain the analytical expression for the FWHM of the final population peak in state |1〉, we have considered, as in [5

5. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B: At. Mol. Opt. Phys. 39, 3437 (2006). [CrossRef]

], that |〈1|D(υ)〉|2 = 1/2 for υ = FWHM/2. Using the profiles given in (2) and (3), the FWHM for CPT is
FWHMCPT=λ2NA2δπ(2R+1)1/2.
(5)

Figure 2 shows the ratio between the analytical FWHM obtained for SLAP [Eq. (4)] and CPT [Eq. (5)] as a function of R for different values of k. From the figure, we can see that in the whole range of parameters considered, the peak obtained with SLAP is significantly narrower than the one with CPT. Note that the adiabatic nature of the SLAP technique allows to increase the final resolution by increasing the time delay T, while fixing the intensities.

Fig. 2: Ratio between the FWHM using SLAP and CPT techniques as a function of R, for k = 0.1 (blue solid line), k = 0.4 (green dashed line), and k = 0.9 (red dotted line).

3. Numerical results

In the following, we are interested in comparing our scheme with the STED microscopy technique [see Fig. 3(a)]. In the STED technique, two beams, the exciting (E) and the depletion (D) lasers, interact with an organic fluorophore, with a time delay Δt. Typical values for Δt are some hundreds of ps, larger than the vibrational relaxation time τ (∼ps) but much shorter than the fluorescence time τfl (∼ns) of the transition n1n0. First, the E field excites all the population to state n1vib, which rapidly decays to n1. Next, the D field, which has a doughnut-like spatial profile, produces a spatial depletion of the population in n1 by stimulated emission. Out of the node, the excited population is removed resulting in fluorescence inhibition, and reducing the width of the effective PSF. Note here that the main distinctive feature of SLAP with respect to general RESOLFT techniques, e.g., STED, is the adiabatic nature of the state transfer process, which as discussed below, confers robustness and flexibility on our method.

Fig. 3: (a) STED technique. Top: Fluorophore energy levels interacting with the exciting (E) and the depletion (D) fields, and their decay rates. Bottom: Pulse temporal sequence. (b) Analytical (solid line) and numerical (crosses) values for the FWHM of the population peak in |1〉, using SLAP, as a function of R. Inset: Spatial profiles of pump (P) and Stokes (S) Rabi frequencies for R = 150. (c) Numerical results of the population p1(x) in |1〉 for SLAP using different values of R, and the population n1(x) in the first excited vibrational level of Rhodamine B for STED typical values (see text).

In Fig. 3(b), values for the FWHM of the final population peak obtained from numerical simulations using SLAP (crosses) and the analytical curve (solid line) given by Eq. (4) using A = 20 are represented. For the simulations, we have used the density-matrix formalism for a Λ-system with degenerated ground states with the following parameter setting: γ21 = γ23 = 2π × 6.36 GHz, ΩS0/γ21 = 1.5, σ = 100 ps, T = 1.5σ, NA = 1.4, and λ = 490 nm. Figure 3(c) shows the final population p1(x) in |1〉 using the SLAP technique for R = 10 (dashed line), R = 50 (dotted line) and R = 300 (dotted-dashed line), marked with vertical arrows in Fig. 3(b). In addition, the population n1(x) using the STED technique (black solid line) is also shown. For the STED simulation, we have used rate equations for the Rhodamine B dye with intensity profiles of the exciting and depletion pulses corresponding to Eq. (2) and Eq. (3), respectively, and typical values [3

3. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780 (1994). [CrossRef] [PubMed]

] for the absorption cross sections σcs = 10−17 cm2, peak intensity of the depletion laser hDpeak=1300MW/cm2, τ = 1 ps, τfl = 2 ns, Δt = 90 ps, σ = 100 ps, NA = 1.4, λE = 490 nm, and λD = 600 nm, obtaining FWHM = 65.2 nm. Note that the final peak in STED does not reach unity due to the loss of population by fluorescence while depletion acts. This does not occur in SLAP, since the final peak corresponds to the population in a ground state.

4. Conclusions and perspectives

In conclusion, we have presented a proposal to implement nanoscale resolution microscopy using the SLAP technique. We have derived an analytical expression to estimate the lateral resolution and we have compared it with the corresponding one for the CPT case, showing that SLAP yields a better resolution. In both cases, the resolution can be improved by increasing the pump intensity ΩP02, provided ΩS0 is kept constant. This behavior is similar in STED microscopy, whose resolution improves by increasing the intensity of the depletion laser. Then, we have performed a numerical comparison between the STED technique using typical parameter values and the SLAP technique with Rabi frequencies of the order of GHz, obtaining a similar resolution in both cases.

Acknowledgments

We acknowledge David Artigas for fruitful comments, and funding from the Spanish Ministry of Economy and Competitiveness under Contract No. FIS2011-23719, and from the Catalan Government under Contract No. SGR2009-00347.

References and links

1.

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. 9, 413 (1873). [CrossRef]

2.

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol. 21, 1347 (2003). [CrossRef] [PubMed]

3.

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780 (1994). [CrossRef] [PubMed]

4.

S. W. Hell and M. Kroug, “Ground-state-depletion fluorscence microscopy: a concept for breaking the diffraction resolution limit,” Appl. Phys. B 60, 495 (1995). [CrossRef]

5.

G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B: At. Mol. Opt. Phys. 39, 3437 (2006). [CrossRef]

6.

A. V. Gorshkov, L. Jiang, M. Greiner, P. Zoller, and M. D. Lukin, “Coherent quantum optical control with subwavelength resolution,” Phys. Rev. Lett. 100, 093005 (2008). [CrossRef] [PubMed]

7.

D. D. Yavuz and N. A. Proite, “Nanoscale resolution fluorescence microscopy using electromagnetically induced transparency,” Phys. Rev. A 76, 041802(R) (2007). [CrossRef]

8.

K. T. Kapale and S. Agarwal, “Subnanoscale resolution for microscopy via coherent population trapping,” Op. Lett. 35, 2792 (2010). [CrossRef]

9.

H. Li, V. A. Sautenkov, M. M. Kash, A. V. Sokolov, G. R. Welch, Y. V. Rostovtsev, M. S. Zubairy, and M. O. Scully, “Optical imaging beyond the diffraction limit via dark states,” Phys. Rev. A 78, 013803 (2008). [CrossRef]

10.

J. Mompart, V. Ahufinger, and G. Birkl, “Coherent patterning of matter waves with subwavelength localization,” Phys. Rev. A 79, 053638 (2009). [CrossRef]

11.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003 (1998). [CrossRef]

12.

D. Viscor, J. L. Rubio, G. Birkl, J. Mompart, and V. Ahufinger, “Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage,” Phys. Rev. A 86, 063409 (2012). [CrossRef]

13.

A. P. Alivisatos, “Semiconductor clusters, nanocrystals, and quantum dots,” Science, New Series , 271, 933–937 (1996).

14.

X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S. Weiss, “Quantum dots for live cells, in vivo imaging, and diagnostics,” Science 307, 538 (2005). [CrossRef] [PubMed]

15.

U. Hohenester, F. Troiani, E. Molinari, G. Panzarini, and C. Macchiavello, “Coherent population transfer in coupled semiconductor quantum dots,” Appl. Phys. Lett. 77, 1864 (2000). [CrossRef]

16.

J. Fabian and U. Hohenester, “Entanglement distillation by adiabatic passage in coupled quantum dots,” Phys. Rev. B 72, 201304(R) (2005). [CrossRef]

17.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262 (2000). [CrossRef]

18.

S. E. Irvine, T. Staudt, E. Rittweger, J. Engelhardt, and S. W. Hell, “Direct light-driven modulation of luminescence from Mn-Doped ZnSe quantum dots,” Angew. Chem. Int. Ed. 47(14), 2685–8, (2008). [CrossRef]

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(110.0180) Imaging systems : Microscopy
(270.0270) Quantum optics : Quantum optics

ToC Category:
Microscopy

History
Original Manuscript: June 17, 2013
Revised Manuscript: August 16, 2013
Manuscript Accepted: August 16, 2013
Published: September 12, 2013

Virtual Issues
Vol. 8, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Juan Luis Rubio, Daniel Viscor, Veronica Ahufinger, and Jordi Mompart, "Nanoscale resolution for fluorescence microscopy via adiabatic passage," Opt. Express 21, 22139-22144 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-19-22139


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat.9, 413 (1873). [CrossRef]
  2. S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol.21, 1347 (2003). [CrossRef] [PubMed]
  3. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett.19, 780 (1994). [CrossRef] [PubMed]
  4. S. W. Hell and M. Kroug, “Ground-state-depletion fluorscence microscopy: a concept for breaking the diffraction resolution limit,” Appl. Phys. B60, 495 (1995). [CrossRef]
  5. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B: At. Mol. Opt. Phys.39, 3437 (2006). [CrossRef]
  6. A. V. Gorshkov, L. Jiang, M. Greiner, P. Zoller, and M. D. Lukin, “Coherent quantum optical control with subwavelength resolution,” Phys. Rev. Lett.100, 093005 (2008). [CrossRef] [PubMed]
  7. D. D. Yavuz and N. A. Proite, “Nanoscale resolution fluorescence microscopy using electromagnetically induced transparency,” Phys. Rev. A76, 041802(R) (2007). [CrossRef]
  8. K. T. Kapale and S. Agarwal, “Subnanoscale resolution for microscopy via coherent population trapping,” Op. Lett.35, 2792 (2010). [CrossRef]
  9. H. Li, V. A. Sautenkov, M. M. Kash, A. V. Sokolov, G. R. Welch, Y. V. Rostovtsev, M. S. Zubairy, and M. O. Scully, “Optical imaging beyond the diffraction limit via dark states,” Phys. Rev. A78, 013803 (2008). [CrossRef]
  10. J. Mompart, V. Ahufinger, and G. Birkl, “Coherent patterning of matter waves with subwavelength localization,” Phys. Rev. A79, 053638 (2009). [CrossRef]
  11. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys.70, 1003 (1998). [CrossRef]
  12. D. Viscor, J. L. Rubio, G. Birkl, J. Mompart, and V. Ahufinger, “Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage,” Phys. Rev. A86, 063409 (2012). [CrossRef]
  13. A. P. Alivisatos, “Semiconductor clusters, nanocrystals, and quantum dots,” Science, New Series, 271, 933–937 (1996).
  14. X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S. Weiss, “Quantum dots for live cells, in vivo imaging, and diagnostics,” Science307, 538 (2005). [CrossRef] [PubMed]
  15. U. Hohenester, F. Troiani, E. Molinari, G. Panzarini, and C. Macchiavello, “Coherent population transfer in coupled semiconductor quantum dots,” Appl. Phys. Lett.77, 1864 (2000). [CrossRef]
  16. J. Fabian and U. Hohenester, “Entanglement distillation by adiabatic passage in coupled quantum dots,” Phys. Rev. B72, 201304(R) (2005). [CrossRef]
  17. P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett.77, 262 (2000). [CrossRef]
  18. S. E. Irvine, T. Staudt, E. Rittweger, J. Engelhardt, and S. W. Hell, “Direct light-driven modulation of luminescence from Mn-Doped ZnSe quantum dots,” Angew. Chem. Int. Ed.47(14), 2685–8, (2008). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1: Fig. 2: Fig. 3:
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited