Anti-Stokes fluorescence refrigeration has a fascinating application prospect, so it has been paid attention to immediately since Pngsheim was proposed in 1929. In recent years, in particular, people have made some breakthroughs in anti-Stokes fluorescence cooling Eppstein 2.1995, and in 1999 FinkeiPen et al. observed laser cooling in semiconductor materials. Based on the above studies, we studied the micromechanism of anti-Stokes fluorescence refrigeration from the perspective of a single molecule (ion), proposed the concept of "single molecule-photon pump" 19105, and established a single molecule-photon pump. Refrigeration theory. The single-molecule photon pump is abbreviated as: SMPC (Single Molecular Photon Clyocooler). In this paper, we use the concept of quantum transition to study the phenomenon that a molecule (or ion) participates in the transition under the action of the light field, so as to study the thermodynamic behavior of SMPC excited by different energy photons. We study these issues in the most general sense and summarize the general laws. 2 - General Discussion In the previous work, we discussed the quantum transitions of Yb3+ ions as a single-molecule photon pump and obtained some laws, but it is not a very common law. From those works, we have obtained the following conclusion: Under a special physical environment, a molecule or ion will produce anti-Stokes fluorescence refrigeration effect under the laser excitation of a special wavelength. It is totally different from the traditional concept of refrigeration. Photon is used as a power provider and energy fund project: National Key Basic Research and Development Program (973 Rare Earth G1998061320) Key Chinese Academy of Sciences Foundation; National Natural Science Foundation of China (59872042) Funding Project Delivery The role of the person. For a single-molecule photon pump, cooling or heating is a probable behavior. Proper selection of the excitation wavelength is the key to achieving SMPC. SMPC can produce cooling effect when it is in the ground state and excited state, and it has stronger cooling ability when it is in the ground state. The significance of the SMPC concept lies in the discovery of the smallest refrigeration pump that the physical world can achieve and control. We will discuss the more general situation below. In order to more clearly illustrate the problem, we imagine a luminescent center with the structure of the illustrated energy level. Both the ground state and the excited state consist of 11 sub-levels. The energy gap (AE) between the ground state and the excited state is so large that the de-excitation of the excited state is achieved in the form of fluorescence radiation, that is, the radiative transition process is the only de-excitation process, and the probability of no radiation transition process is zero. Similarly, we assume temperature conditions are normal or cold. Under such conditions, thermal excitation cannot excite the luminescent center from the ground state to the excited state (the probability is very small, negligible). The transition (relaxation) between the internal sub-energy levels of the ground state or excited state is accomplished by thermal excitation, ie the phonons participate in the transition process between the sub-energy levels. In addition, we assume that the ground state or excited state has a sub-level spacing of a and a single frequency approximation of the phonons, while assuming that all phonon energy is a from the lower sub-level to the higher sub-level relaxation The phonons are absorbed, and the phonons are released from the higher sublevel to the lower sublevel. Absorbing phonons, ie increasing the thermal vibration of the matrix around the SMPC, lowers the temperature of the surrounding matrix; releasing the phonons, which increase the thermal vibration of the matrix around the SMPC, increases the temperature of the surrounding matrix. The imaginary single-molecule-photon pump energy level structure is convenient for research. We have also made the following assumptions in theoretical processing: the luminescent center is in the light field where the photon energy is En=ΔE+na, and n is an integer. The pump light has very good monochromaticity and therefore the selectivity of the excitation is very good. The initial state of the pump light excitation condition can absorb an E photon transition to the corresponding energy level of the excited state. After the occurrence of absorption transitions and radiative transitions, we assumed that the redistribution time between the multiplet neutron energy levels is very short and much shorter than the lifetime of the excited state. In addition, we also assume that the probability of each sub-level from the excited state down to the ground state is the same when the photon transition is excited. Of course, the latter assumption is very weak and many situations do not fully satisfy such conditions. In general, when the luminescent center transitions from the excited state to the different sub-energy levels of the ground state, it has a different branching ratio, which has a great influence on the efficiency of the fluorescent refrigeration. As a general discussion, we have made the assumption that all sub-levels are treated equally, but we must consider the effect of branch comparison on absorption and emission when dealing with practical problems. We use different wavelengths of light for excitation. The excitation energy is divided into k+1 species from low to high, and the photon energy is: At the same time, it is assumed that the excitation light has very good monochromaticity. The light center shown in the figure was excited with this k+1 energy light, and computer simulation was performed on it. The specific simulation process is shown in the appendix. From the simulation results, it can be seen that the thermodynamic effects of the ground state and the excited state during light absorption and emission are different. 3 Thermodynamic behavior of the ground state For the energy level structure shown, we first use E0 (=AE) photons for excitation. E0 is the minimum energy that can excite this luminescent center. Only when the molecule (ion) is in the highest sub-energy level of the ground state can the E0 light be excited to the lowest sub-energy level of the excited state. Under the excitation of AE light, the relationship between the number of phonons in the net absorption of the ground state and the number of fluorescence photon emission when emitting 10 000 fluorescence photons is shown in (a). It gives the number of times that the luminescent center absorbs different numbers of phonons. From the figure we can see that when the fluorescence transition occurs, the number of phonons per ground state is basically the same, and it is uniformly distributed. (b) illustrates the contribution of ground state absorption of different phonon numbers to fluorescence refrigeration. From this we can see that the transitions that absorb more phonons have a greater contribution to fluorescence refrigeration, which is basically a linear relationship. Since we assume that the transitions from the excited state to the ground state are equally probable, the number of sub-energy levels of the ground state involved in the fluorescence emission under the △ photoexcitation is essentially the same (see (a)). The higher the energy level of the child, the more phonons are released after thermal equilibrium, and the lower the energy level, the lower the number of phonons emitted after thermal equilibrium. Or we can say that at the low-energy level, the highest sub-energy level is reached before it can be excited to the excited state, and then the fluorescence is cooled by fluorescence radiation. It is also so strong that the lowest sub-energy level required by any heat-induced excitation to satisfy the optical transition to the highest sub-energy level of the ground state is Qin Weiping, et al.: thermodynamic behavior of single-molecule photonic refrigeration pumps (1 Under the excitation of AE light, the starting point for the transition from the ground state to the excited state is the I 1,10> sub-energy level, and all states in the other ground state energy levels are absorbed by the phonon to reach the I1,10> energy level. Absorption of an AE photon transitions to the excited I2,0> sub-energy level. Therefore, at different ground state level 11, the states on “〉†must absorb different numbers of phonons to be excited by heat to I1, 10 states, and then participate in the optical transition. For example: I 1,0> absorbs 10 phonons; 1,1> absorbs 9 phonons...11,10> absorbs 0 phonons; and then, single molecules enter the excited starting point I1,10> sub-energy states. 4 The thermodynamic behavior of the excited state ΔE is the minimum energy that can excite the luminescent center. Therefore, when just jumping to the excited state, it can only be on the lowest sub-level 12 0 > of the excited state. Since the time taken for each sub-level energy level in the excited state to reach thermal equilibrium is much less than the fluorescence lifetime of the excited state, the luminescent center in the I,0> state is first redistributed in the excited state according to the Boltzmann distribution rule, and then Radiated transitions occur at the sublevels of the ground state. In the process of redistribution, the excited state of the single molecule center will absorb or emit phonons (under this excitation condition, the net thermodynamic effect is absorption of phonons). Specific simulation results show that they absorb different numbers of phonons and occur. The relationship of the number of such absorption. From the figure, we can see that when the fluorescence transition occurs, the frequency of transition of the excited state to absorb different numbers of phonons is different. This is completely different from the result of the ground state. It reflects the dependence of the excited state on the phonons in the Boltzmann distribution. The greater the number of phonons absorbed by each transition, the smaller the number of occurrences of such absorption and the exponential decline. As in the case of the ground state, there is no net phonon release in the excited state under AE excitation. This is because AE is the minimum energy that excites the center of this single molecule. (b) The relationship between the number of absorbed phonons per time and the total number of absorbed phonons when a single molecule photon pump is in an excited state. It is completely different from the situation of the ground state. The process of absorbing a few phonons such as one and two plays a major role, and the process of absorbing multiple phonons is relatively rare. From the comparison with , we can see that the cooling capacity of the ground state under the excitation of AE light is far greater than the excited state. 5 Ei Photon Excitation - Thermodynamic Behavior After Increasing Photon Energy We increase the energy of the excited photon and use a photon with energy E1 = AE+a to excite the single molecule center. At this time, there are two possible absorption processes: At this time, the single molecule center can be excited to the I20> state of the excited state at the sub-energy level I1 9 >, and it is at the probability of the base state energy level I1, 9>. The chance of being at child level I1, 10>. Therefore, the absorption process from the sub-energy level I1,9> to the excited state I2,0> will dominate. When the single molecule center is excited to the excited state, two kinds of sub-energy states can exist in the initial state. When the Boltzmann distribution is excited, two results will appear when the ground state condition is LU number/per transition. The initial thermal distribution in the I2,0> state is the same as in the case of the E0 photon excitation discussed above; the initial heat distribution in the I2 1 > state will have a chance to return to the 120> state, thus releasing the phonons. If 1 and 1 in the abscissa indicate 1 phonon is released. When the optical radiative transition occurs, the probability of returning to the substates of the ground state is the same. Since the energy at the 11th, 9th sub-level can be excited by the energy of E1 to the excited I20> sub-level, the state of the I1,10 at the sub-state has a chance to return to the excited state. 11,9 states. Therefore, such a process will release a phonon. Based on the above discussion, we can see that the number of transitions absorbing 0 to 9 phonons is basically the same, which is the same as the case of E0 light excitation. The number of absorption of 10 phonons is greatly reduced, and the process of releasing one phonon appears. This is due to the number of times that the ground state absorbs different phonon numbers when excited by I1,10>Ei and undergoes fluorescence transitions; (b) The absorption of different phonons by the ground state contributes to the fluorescence refrigeration, and the excited state is excited by (a)E1. The number of times the excited state absorbs different phonon numbers when excited and undergoes fluorescence transitions; (b) The contribution of different states of the excited state to fluorescence refrigeration. Qin Weiping, et al.: Thermodynamic behavior of single-molecule photonic refrigeration pumps (1) The state of the class has a great chance to return to the 9tz state when the Boltzmann distribution. The number of times of absorption of 10 phonons and the number of releases of 1 phonon are added. The number of phonon participations of the two processes obtained is the same as that of other processes, as shown in (a). (b) indicates the total number of phonon participations in the process of absorbing and releasing phonons. The curves in the figure show that the process of absorbing 9 phonons in various processes contributes the most to the fluorescence refrigeration. The middle part of the curve is basically a straight line. Under Ei photoexcitation, the thermodynamic effect of the excited state of a single molecule center is shown in (a). A 1 on the horizontal axis indicates that 1 phonon is released at the center of each single molecule of the optical transition. This is because when the single molecule center enters the excited state, the initial state is the I21> state. In the Boltzmann distribution, there is a considerable chance of returning to the I2O> state and releasing one phonon at the same time. From (b) we can see that the process of small number of phonons participating in E1 photon excitation plays a greater role in thermal effect. This effect tends to decrease exponentially as the number of participating phonons increases. The same as the case of E excitation, that is, the process that does not absorb phonons or release phonons accounts for the largest proportion. The second is the process of absorbing a phonon or releasing a phonon. 6 E2 and Higher Energy Photon Excitation 2a At this time, there are three possible absorption processes: Excitation, ground state, Lue participation number/per transition, and at sub-level I1, 8> can be excited to the excited state. 120's sub-level energy. The probability of being in the ground state sublevel I1,8> is greater than the probability of being in the sublevel I19>, I110> state. Therefore, the absorption process of the I2,0> state transitioning from the sub-level I1,8> state to the excited state will dominate. When the single molecule center is excited to the excited state, the initial state of the excited state can be three kinds of sub-energy states, and three results occur when the Boltzmann distribution is performed. The initial heat distribution in the 12 0 > state is the same as the E 0 photon excitation discussed earlier; the initial heat distribution in the I 2 1 > state will have a certain probability of returning to the I 20 > state, thus releasing a phonon. The initial heat distribution in the 12 2 > state will have a certain probability of returning to the I20〉 and 121〉 states respectively, releasing two and one phonons. For example, the abscissa one by one, one by one indicates the number of phonons released. When the optical radiative transition occurs, the probability of returning to each sub-level of the ground state is the same. Since at the level of I1,8> or I1,9>, the light with energy E2 can be excited to the I2 0> or 121> level of the excited state, respectively, while the I110> and I19> energy in the ground state. The state of the class has a certain chance to return to the I1 1,8> state. Therefore, such a process will release two or one phonon. According to the above description, we get the following simulation results, see. From (a) we can see that the number of processes that absorbed 9 or 10 phonons in one optical transition decreased, and the process of releasing two phonons appeared. The process of absorbing 8 phonons at a time has the largest cooling contribution. (a) The number of times the ground state absorbs different phonon numbers when E2 stimulates and undergoes fluorescence transitions; (b) The contribution of ground state absorption to different phonon numbers for fluorescence cooling (a) When E2 stimulates, phonons in the excited state participate in the The frequency did not change substantially, but there was a process of releasing two phonons. condition. It can be seen from this that there is also a leap in the excited state. We noticed the symmetry of (a) and (b) and released the process of moving two phonons. From the comparison of the frequency of transitions between the two phonons in (b) and 7(b) and the basic phase of absorbing two phonons we can see! The process of absorption of phonons in sub-optical transitions; the frequency of transitions for emitting one phonon is approximately the same as that of luminescence that absorbs one phonon, showing the feature that the point where the phonon participation number is equal to zero is symmetric. Therefore, the thermodynamic effects produced by the above four processes cancel each other out. This offset is not strictly non-thermal and heat-absorbing. Their mutual cancellation does not mean that there is no phonon participation. This mutual offset is a fluctuation characteristic. Under photon excitation with energy of E2, for the excited state, what really affects the thermodynamic effect is the process of absorbing phonon number 3 or more. Although the probability that the number of phonons absorbed or emitted by each optical transition is less than 3 is large, their thermal effects cancel each other out; the probability of occurrence of the process where the number of phonons absorbed by each optical transition is greater than or equal to 3 is small. However, it can produce a net cooling effect. Further increasing the energy to stimulate photons will be more obvious. In the middle, we give the simulation results of E(rE17 photons with different energy excitations. They show a strong regularity. From the figure we can clearly see that in the low energy (E~E5) photon Under excitation, SMPC takes more phonons through thermal relaxation of the ground state in the process of excitation light absorption-fluorescence radiation; the amount of phonons taken away by the thermal relaxation of the excited state is less. In the thermal relaxation of the excited state, the number of phonons taken away within the range of a certain excitation photon energy (E5~Ek) is basically constant, and the phonon absorption and phonon emission are symmetrically distributed. When the energy of the excitation photon is greater than or equal to E6, the number of phonons emitted from the thermal relaxation process of the ground state begins to be greater than the number of absorbed phonons. At this time, the ground state of the single molecule begins to generate heat. When the energy of the excitation photon is greater than or equal to E11, the number of phonons emitted by the thermal relaxation process of the excited state begins to be greater than the number of absorbed phonons, and the thermal relaxation process of the excited state begins to produce a heating effect. The relationship between the number of phonons participating in each transition and the total number of phonons under excitation of photons of different energies. The left picture shows the change of the ground state. The right picture shows the change of the excited state. Qin Weiping, et al.: The thermodynamic behavior of a single molecule-photon refrigeration pump (I) Under a special physical environment, a molecule or ion is excited by a laser at a specific wavelength. Anti-Stokes fluorescence refrigeration effect will result. We use a general physical model to simulate the thermodynamic behavior of a single molecule (or ion) under excitation with different energy photons. This simulates the frequency and number of phonons participating in absorption transitions and radiative transitions of a single molecule (or ion). The result is that it is thermally relaxed when it is in the ground state or excited state. Through the above research, we have obtained the following conclusions: The ground state has a strong cooling capacity, and under the excitation of ~ E5 photon produces fluorescence refrigeration effect; 5 photon excitation reaches the maximum value of refrigeration, and E6 excitation generates a lot The heat; further increase the energy of exciting photons, the heat generated by a single molecule will further increase, and thus become a heat source. When a single molecule is in an excited state and undergoes thermal relaxation, there is a certain ability to absorb phonons under the excitation of small energy photons, but as the energy of the excitation photon increases, the excited state absorbs phonons and emits phonons. Out of strong symmetry. This symmetry is maintained until Ei is excited. Ei excites the transition from the lowest sublevel of the ground state to the lowest sublevel of the excited state. When the excitation photon energy is greater than or equal to the Eli excitation, the single molecule in the ground state can be excited to the sub-lower energy level of the excited state. Therefore, the relaxation in the excited state must generate a large number of phonons. Therefore, we can conclude that in our model, the sub-energy level of the excited state contributes less to cooling than the sub-level of the ground state. Especially when the excitation photon energy is within a certain range, the thermal relaxation process of the excited state has no effect on the single-molecular refrigeration pump. Therefore, when the anti-Stokes fluorescent refrigerating material is selected, the ground state energy level of the luminescence center may be more important. Here we give a specific simulation calculation process for a single molecule - photon pump simulation calculation flow chart. First, we assume that the single-molecule center shown is initially in the ground state I1,0> state, ie, g=0, and at the same time, a narrow-band high-intensity laser with energy E=AE+kaa is a positive integer) is illuminated in this sheet. At the center of the molecule. Due to phonon interaction (thermal excitation), the single molecule center jumps between the 11 sub-levels of the ground state. The long-term average of this jump conforms to the Boltzmann distribution rule, or the result of each jump follows the Boltzmann distribution law. From the lower sub-energy level to the higher sub-energy level, the single molecule center absorbs phonons. For example, the thermal excitation process of I1,0>,1,2> absorbs two phonons; in turn, the thermal excitation process of I1,2>,1,0> emits two phonons. We use the program to record the number of phonons absorbed or released by each jump, absorb one phonon as +1, and release one phonon as a 1. This heat distribution is very fast, and the average of each distribution is completed. The time is femtosecond or picosecond. When a single molecule center jumps to I1,m>(g=m, m>10-k), it can absorb a photon and jump to the 12> sub-level of the excited state.
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Thermodynamic Behavior of Single Molecule-Photon Refrigeration Pumps (I)
Thermodynamic Behavior of Single Molecule-Photon Refrigeration Pumps (I)
Core Tip: Anti-Stokes Fluorescent Refrigeration has a fascinating application prospect, so it was immediately taken into account by Pngsheim since its introduction in 1929. Especially in recent research, people have achieved some breakthrough employment in anti-Stokes fluorescence refrigeration.