Spectral jump

To date, the spectral jump phenomena have been one of the most exciting experimental observation in single mole-cule spectroscopy. An example of spectral jump is shown in Fig. 32. The displayed molecule is spectrally jumping be-tween two states during experiment.

Anderson et al.⁴⁶and Phillips⁴⁷independently intro-duced a TLS (two-level system) model explaining the “anom-alous” behavior of the specific heat and thermal conductivity in glasses. TLSs are the simplest representation of the multi-dimensional energy surface. At any point within the sample, certain groups of atoms or molecules have access to two (or more) potential energy minima and can switch between these two minima by a tunneling process as, for example, ammonia molecule does. A TLS involves an asymmetric double poten-tial well, (see Fig. 33). The surface consists of three regions Fig. 25. “Sample sandwich” for Stark effect experiments. Notice that ITO coated cover glasses and an additional pinhole foil

is used on the emission side.¹³

Fig. 26. In the “sample sandwich” configuration of Stark effect experimets, the laser propagation directionr

k is always parallel to r

Eext. The polar-ization r

P is rotated byw around the y-axis to minimize the anglea betweenr

P and the transi-tion dipole moment of a molecule.¹³

represented by L, R and M. Transitions between the two wells represent changes in the local structure of the material. One or several TLSs distributed randomly in the matrix might in-teract with a single molecule. At helium temperatures the thermal energy is lower than the potential barrier so that a transition between the wells is caused by tunneling along a generalized coordinate Q_l, which characterizes the degrees of freedom involved. The Q_lcoordinate might represent the po-sition of one atom or a center of mass of a larger system, or a rotation angle of some group of atoms. Although the effects of TLSs has been observed in a wide variety of chemically different systems for two decades, the nature of these degrees of freedom is not known. However, to explain spectral dy-namics of single molecules at low temperature, the two-level system, is often used.^48-53

In the system represented by Fig. 33, the Hamiltonian operator is approximately given by

(22) Here $HLand $HRrepresent the Hamiltonian operator of L and R, respectively.

For the case in which vibrational relaxation is much faster than reaction, a thermal average should be introduced to write the transition probability W from L to R as^54-56

(23) where PLrepresents the Boltzmann distribution, and XRand XLdenote the wavefunctions for R and L, respectively.

Sup-500 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Latychevskaia et al.

Fig. 27. Sample-holder with electrodes. (a) Picture of the sample-holder. (b) Teflon washer with chip. A drop of sample is placed between the chip and a microscope slide. (c) Pyrex chip with interdigitated electrodes.

Fig. 28. (a) The geometry of the electric field on the chip with electrodes.r

Eext- externally applied electric field vector,r k -the laser propagation vector, r

P is the laser polarization vector, and r

H is the magnetic component of the laser beam.

(b) Sum of images recorded in white and laser light. The black stripes are the chip electrodes. The bright spots are the fluorescence signals from single molecules. The crystal structure of the sample can be seen.

L M R R M L

ˆ ˆ ˆ ˆ ˆ ˆ ˆ .

H=H +V +V =H +V +V

2

L R MR L R L

L R

2 | ˆ | ( )

W = _hp

åå

P X V X d E -E

pose that the transition between L and R is through coupling of one promoting model (the reaction coordinate being Ql), and that we can write the wavefunctions as

(24) and

(25)

where Qiis the coordinate of the i-th mode in L and Q_i^'is that of the same mode in R, whileuⁱandu¢iare the vibrational quantum numbers of those modes, respectively.cLviis the wavefunction of the i-th mode in L, and so on. Here we as-sume that they are harmonic modes. Substituting Eqs. (24) and (25) into Eq. (23) yields

(26) where the time-correlation functions Gl(t) and Gi(t) are given Fig. 29. Molecular linear Stark effect. The most intensely fluorescing molecules are labeled with “A” to “F”. The dashed line

indicates the mirror symmetry axis in the experiment. The rectangular inset, which is a blown up section of the cir-cled region, shows a spectral jump in Stark trace D. 500 sweeps, accumulated with an electric field ramp repetition rate of 433 Hz, were summed up to obtain one scan at a fixed laser frequency. The laser frequency step size wasDn^L

= 48 MHz.

L Lvi Lv

' ( _i) ( ),

i

X ì c Q üc Q

= í ý

î

Õ

þ ^{l l}

i

R Rv' Rv'

' ( ) ( '),

i i

X ì c Q' üc Q

= í ý

î

Õ

þ _l ^l

0

RL '

2 ^it ( ) _i( )

i

W p ^¥dt e^w G t G t

= _h

ò

-¥ ^l

Õ

by

(27) and

(28)

More complicated cases can be also be treated in the same manner.

For displaced harmonic oscillators, Gi(t) can be ex-pressed as^56,57

(29) wherewⁱis the vibrational frequency of the i-th mode, Siis the

502 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Latychevskaia et al.

Fig. 30. Quadratic Stark effect measured on four single pentacene molecules in p-terphenyl matrix.⁴¹The circles denote the resonance position of a single molecule.

Fig. 31. Two single Tr and DPNP molecules showing a higher order Stark effect. The lower parts of the picture show molecu-lar spectra in the absence of an external electric field. The scans with and without external field were performed in al-ternating fashion in order to eliminate laser drift from the data.

( ) exp (2 1) {( 1) ^{it i it i}} ,

i i i i i i

G t = éë-S n + +S n + e^w +n e^-w ùû

Rv ,Lv

2

Lv Rv Lv

' '

'

( ) | ˆ |

it

G t P VMR e^w

u u

c c

=

åå

^l _l ^{l l l}

l l

l

Rv ,Lv i i

2

Lv Rv Lv

' '

( ) _i | ^{i i}.

i i

it

G ti P e ^w

u u

c c

=

åå

^'

coupling constant, and niis the thermal-average occupation number of that mode. That is,

(30) Using Eq. (29) we obtain

(31)

For the strong coupling case, we can use the short-time

ap-Fig. 32. Resonance frequency changes for a single terrylene molecule. (a)-(f): Six sequential fluorescence excitation spectra with 40 s per scan, 0.32 W/cm²laser intensity, and the time between scans varying from 2 to 10 min. Inset: gray-scale image of continuous “fast” 1 GHz (only 90% plotted) excitation spectra. The x-axis is the laser frequency detuning, the y-axis corresponds to the time axis (scans are plotted consecutively from bottom to top), and the darkness of the image represents the fluorescence intensity. There are a total of 2220 scans acquired over 5683 s, with 10 ms/point, 256 points/scan, and 1.1 W/cm²probing intensity.

Fig. 33. The two-level model often used in treating the spectral jump phenomena.

Fig. 34. The particular potential energy surface used in the model of spectral jump in this work.

{ }

0 RL

2 ( )

exp _i (2 _i 1) ( _i 1) ^{it i iti}

i

W dt G t

it S n n e^w ne ^w

p

w

¥ -¥

-=

é ù

´ êë + - + + + + úû

ò

å

h l

(

^{/ B}

)

' 2

( ) ; 1/ 1 .

2

i k T

i

i i i i

S =w Q -Q n = e^hw -h

proximation:

(32) In the classical limit, Eq. (32) becomes Arrhenius equation.

From the above treatment we can see that up to this point, the details of the potential surfaces along the reaction coordinate Q_lis not specified. For this purpose, we consider a particular case, That is, G_lshows an isotope effect. For example. for hydro-gen H and deuterion D, we have

(39) In other words, the transition is slower for heavier isotopes.

Thus a correct tendency is predicted.

Asymmetric double well model can also be solved in the similar manner, and it is more suitable for describing the spectral jump phenomena in SM, but the algebra involved is more complicated so we do not discuss it further here.

504 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Latychevskaia et al.

Fig. 35. Frequency shifts of terrylene in hexadecane interpreted by TLS model.

2

3. SINGLE MOLECULES AT ROOM TEMPERATURE

在文檔中 Single Molecule Spectroscopy (頁 23-29)