Spontaneous Emission Of Multi-level Atoms Driven By Laser Fields

In this thsis, we mainly investigate how the spontaneous emission (SE) spectra of multiple-level atom evolve when changing the frequencies of the driving fields. The effect of certain decay rate is considered too. There are two parts: one is that the investigated SEs have levels coupled by optical field, i.e. resonance fluorescence; the other is that the investigated SEs have levels not coupled by optical field. The system (atom plus fields) of the later has the character of Spontaneously Generated Coherence (SGC). Then we can call the later: SE under similar SGC.In part one, we investigate the SE spectra of three three-level atom driven by two fields and one four-level atom driven by three fields one by one.Here, take the three-level V-type atom for instance, we analyze the SE spectra in detail. Two strong fields withω_a,Ω₁ andω_b,Ω₂ are coupled to levels |1>(?)|2> and |1>(?)|3>, respectively. Corresponding detuningsareΔ₁ andΔ₂.We can obtain the Hamiltonian and equations of motion of the matrix elements of the system in terms of Quantum Optics. Then we calculate the SE spectra of the transition from state |3> to |1> in the light of QuantumRegression Theorem and Laplace transformation.We are mainly interested in the effect of the field detunings on the SE spectra, we assumeΩ₁ =8,Ω₂ =6,Γ₂₁ =0.5,Γ₃₁ = 1(MHz) . HereΓ_ij is thespontaneous decay rate from state |i> to |j>.without decayΓ₂₃ orΓ₃₂ (a) and with decayΓ₂₃ orΓ₃₂ (b)When two-photon resonance (Δ₁ =Δ₂ =Δ) is satisfied, the SE spectrum is shown in Fig. 2: if there are no decayΓ₂₃ =Γ₃₂ = 0(MHz) between upper states |2> and |3>, the SE spectrum is shown in Fig. 2(a);ifΓ₂₃ =Γ₃₂ = 0.3(MHz), then the SE spectrum is shown in Fig. 2(b). It can beseen that two more inner sidebands appear whenΓ₂₃ orΓ₃₂ are nonzeros.The SE spectra show more feature when two-photon resonance is deviated, shown in Fig.3. KeepΔ₁ = 0 ,Fig.3(a) shows how SE spectrum changes whenΔ₂ varies; keepΔ₂ = 0 , Fig.3(b)shows how SE spectrumchanges whenΔ₁ varies. In general, there are seven peaks in the SE spectrum. But at certain points some peaks superpose resulting in five-peak SE spectrum. In the limit, bigΔ₂ decrease the population of |3>, so the total SE intensity iszero. But, bigΔ₁ decrease the population of |2>, the system equals to atwo-level atom driven by a monochromatic field, so the SE spectrum has three peaks. Furthermore, we find that the intensity of the central peak has anextremum whenΔ₁ =Δ₂ and decrease first then increase to a value when detuning increases, shown in Fig.3 (b).Some characters of the SE spectra can be interpreted via dressed states theory of atom plus fields. In the dressed states, each of the states is dressed into three substates, as shown in Fig.4.There are nine transitions from the upper three substates to the lower three substates. In any circumstance, there are three transitions denoted by "d", "e" and "f" have the same transition frequency toω_b, they superpose into one peak i.e. the central peak. In general, the other transitions do not superpose, so the SE spectra have seven peaks.Compared Fig.5 to Fig.2, we find that whenΔ₁ =Δ₂ andΓ₂₃ orΓ₃₂ arenonzeros two transitions denoted by "b" and "h" do not occur; ifΓ₂₃ =Γ₃₂ = 0(MHz), even another two transitions denoted by "c" and "g" do not occur too. The reasons are: under two-photon resonance, the dressed states |N,0> and |N-1,0> do not have the component of |1>, and becausetransitions only occur from state|2>to |1> and from state |3> to |1>, so in the dressed states, the transitions from upper three substate to |N -1,0> do not occur. IfΓ₂₃ =Γ₃₂ = 0(MHz), further calculation shows that there is nopopulation on state |N,0>, so the transitions from state |N,0> to the lowerdressed states do not occur too.When two-photon resonance is not satisfied, relative frequencies of the transitions are shown in Fig.6.Further analysis shows that at certain point the SE spectra have five-peak configurations: corresponding oneΔ₁, there are threeΔ₂ of that result; whilefor oneΔ₂, when |Δ₂| is small there is only one suchΔ₁, when |Δ₂| increases to certain value there are two suchΔ₁, further increase of |Δ₂| results inthree suchΔ₁.Moreover, we investigate the SE spectra of three-level Lambda-type and Ladder-type atom driven by two monochromatic fields, so does four-level Y-type atom driven by three monochromatic fields. They have the similar features. For the three-level Lambda-type, when two-photon resonance is satisfied, the system evolves into Coherent Population Trapping, resulting in quenching of the SE. In part two, we firstly show that a four-level anti-Y-type atom driven by two coherent fields has the character of SGC. Then we investigate the SE spectra of that system. At last, we experimentally demonstrate the feasibility of acquiring SGC in dressed states via measuring the absorption of the system.Two strong fieldsω_a,Ω₁ andω_b,Ω₂ are coupled to transition |1>(?)|2> and |2>(?)|3> respectively. Corresponding detunings areΔ₁ andΔ₂.Under dressed states, state 2} split into three levels, noted |±,0>. ThenThe dipoles of the transitions from |±,0> to |4> are:Then, we haveObviously, if only there are two nonzero a₂¹, there are transition-channels with parallel (or anti-parallel) dipoles. The spacings between the dressed states and a₂¹ depend on the intensity and detunings of the driving fields. So suitably choosing these parameters can make the system have the character ofSGC.Below, we analyze the SE spectra from state |2> to |4> . AssumeΩ₁ = 3,Ω₂ = 4,Γ₂₁ =Γ₂₄ = 3,Γ₁ = 0.01,Γ₄ = 0.1(MHz).In general, the SE spectra have three peaks. When two-photon resonance, the total intensity of the spectrum is very small; while, the intensity of the central peak is much bigger when there is small detuning, which is our focus.The three-peak feature of the spectra can be explained that there are threetransitions from dressed states |±,0> to |4>. If the transitions are independent,the total spectrum is the superposition of three peaks. But as shown in Fig.10 (b) and (c), spectral enhancement and SE quenching happen when there is small detuning. They can not be interpreted by linear superposition. The reason is that there is interference between the transitions fromstates |±,0> to |4>.Meanwhile, we wish to confirm the results above. But for some reasons, we have not obtained the SE spectra yet. Compared to measuring SE spectra, absorption can be easily obtained and they have similar characters. We measured the absorption spectra in ⁸⁵Rb. The levels we adopted are shown in Fig. 11 and the experiment is implemented in atomic beam as shown in Fig. 12.The rubidium atomic beam has a diameter of about 3mm in the active zone. DL2 is a diode laser with wavelength 794.97nm, linewidth 1MHz, power 8mW, diameter about 4mm. Ti:Sapphire is a solid laser with wavelength 761.8nm, linewidth 0.5MHz, power 88mW, diameter about 4mm.They are used as coherent fieldsΩ₁ andΩ₂. The probe field is another diodelaser with wavelength 794.98nm, linewidth 1MHz, power 1μW, diameter about 1mm.The measured absorption spectra are shown in Fig.13. One peak of transition from ⁸⁵Rb 5S_1/2, F=3 to 5P_1/2, F=3 was obtained without applying the coherent fields, as shown in Fig.13 (a). The FWHM is about 14MHz, bigger than the natural linewidth. It can be result from residual Doppler broadening of the atomic beam, laser and instruments linewidthes. When the coherent fieldω_b is applied, the single absorption peak splits into two narrower peaks,leaving a deep transparent window in the center, which is the typical Electromagnetic Inducing Transparent (EIT) in three-level Ladder-type atom. The two small windows noted in circle are the effect of levels 5D_3/2, F=3, 2. When both the coherent fields are applied, we get the other three spectra. Under two-photon resonance, the spectrum has a more deep transparent window, as shown in Fig.13 (c). Fig.13 (d) and (e) show the absorptionspectra whenΔ₁ +Δ₂ = 4.5MHz andΔ₁ +Δ₂ = -9MHz,respectively. Theexperimental measurements are in good agreement with the calculation of absorption of system with SGC.To date, we have confirmed that the system of atoms driven by coherent fields has the character of SGC by measuring the absorption spectra of multiple-level system.