BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC VINH ------------ HOÀNG HỒNG KHUÊ ĐIỀU KHIỂN SỰ HẤP THỤ VÀ TÁN SẮC TRONG HỆ NGUYÊN TỬ 87 Rb CẤU HÌNH LAMBDA Chuyên ngành: Quang học Mã số: 62.44.11.01 LUẬN VĂN THẠC SĨ VẬT LÝ Người hướng dẫn khoa học: PGS.TS. ĐINH XUÂN KHOA VINH - 2010  MỤC LỤC Mở đầu Chương 1. Tương tác giữa ánh sáng với hệ nguyên tử  1.1. Nguyên tử hai mức trong trường điện từ   !"# $ %& ' ()*+, $!-./,% 1.2 Nguyên tử ba mức trong trường điện từ$ 0-123 Chương 2. Điều khiển sự hấp thụ và tán sắc trong hệ nguyên tử 87 Rb cấu hình lambda' 2.1 Cấu trúc năng lượng của nguyên tử 87 Rb' !/4-5 6' 78' !/4.-5 6' 789 %!):21;<"=5 6' 78 2.2. Giải phương trình ma trận mật độ cho cấu hình lambda 2.3. Mỗi liên hệ giữa các phần tử ma trận mật độ với cảm nguyên tử9 2.4. HÖ sè hÊp thô cña m«i trêng nguyên tử víi chïm dß 31 2.5. ChiÕt suÊt cña m«i trêng nguyªn tö (hÖ sè t¸n s¾c) 31 2.6. Điều khiển sự hấp thụ và tán sắc% 2.7. Hiệu suất biến đổi độ trong suốt> 2.8. So sánh kết quả giữa cấu hình Λ ,chữ V và bậc thang 0-12% Kết luận chung Tài liệu tham khảo$  MỞ ĐẦU ?    &  @   A    +)  B+  . :  : #C?/DCEFCEEG.H+5IJ KLMC?.N.O*+C"CK+<P .NIJQLC++)B+.::-@ 1&#&.H/D.O8J*+R"+SG.H) TUF*+&.H/D?@<1<-"*5?? 1@8C)5IJKE?V?.F ??<+.OT?.HCH+)B+.P=1< B+1.WIMQI.FCSK5+)B+.P=1<B+ 1.WCSKQX&@<C@=1<.F?.H*+,C&Y PZ[\Z1W?+W11[IWI.WQC@+X.CSR/ <?]+969^_<C@K+, `  ` +<?]+99^_W? &,0+W\0?L.FCa&.H/D.OIbC-.FCa& .N<I?CCa2H+5.1S?+ < (SK&,?.H*+,C&YZ[&CC@ 4;,*I&1;-<F&+CH &?C/S,4;C- :Ec ` ? d 8 `  e + ` "? ` ^%_L. ` 1<+2+ `  d  ? d + e .^_LR e 1 d 1@^3_L]&./" #"- ^9_L a*? ^>_ fGCS+ ,C@Z[<CSK&,?.H*+,C&+) gh?+1Ei&*?.&,? .H*+,C&Y?+&C)/j0*TI? &,V?1W<"#E+IbC-:?1< CK % !,SZ[2<?+1?E S+#aC&54C*<k+?+S#/ K.ID1.W+E1<+l::-@ ! d m n ::C*/CKE? `  d ?.H*+ ,C&Y1<IF&8+,]1@C@1-8T B+.::BW?.F.NR-5IJK E<81?E/#::c82 Li<1+8IΛ oi&p+L,S&,?.H*+,C&YC@ F&CGT+,(E=i/#82 ^6_</#i^9_?1?E/#<LHC)  +,]1@1<CH1X&"*1<.a?.HZ[ .O8JE-C). ?a12]4=CS<,q Điều khiển sự hấp thụ và tán sắc trong hệ nguyên tử 87 Rb cấu hình lambdar !/412]?<G+TCGL-12<<1&+*?L )I:512]l+ !c#8<.T1;-S& +,.W?1;-8aCKL.TC ,.F&8+,]1@RhC-"#   !c!4#8<1*5#+2+2 C)? 6' 788+,]1@/#1+8IY-"*1; -4OC?/D<C?.N, J5C)CSK<C)1&G5 CSKU?.-"*1;-<F&+.TC#+K S&./8-CaC)?.HU?.-"*/#Λ /#i<82  Chương 1 TƯƠNG TÁC GIỮA ÁNH SÁNG VỚI HỆ NGUYÊN TỬ 1.1. Nguyên tử hai mức trong trường điện từ 1.1.1. Tương tác giữa hệ nguyên tử với trường khi không có phân rã Hình 1:s#&+, W?1;-8aCK#&1<+)&1@P&+< ?C+,]1@5&C C@1@?QLMC& YbC@RW+1<aCKP,1<bC@+*8T<+ 5P BE  L QQ?=1@L4# ?+2+2C)c  [ ] H i t L ρ ρ  = ∂ ∂  PQ ?Cc I HHH += > 1<X+1??<G  > H 1<X+1?5&  I H 1<X+1?It*5&+ V?uRh+,]1@<.8-?  > H 1<c         =   > > > W W H PQ !C)?<C@8KItIIEc ( ) rktEE L   −= ω ?. > L P%Q $ TC k  1<h.i.#/# ( ) ' >v − ≈= mk λπ < 8: mr > > − ≈ L#K1/ > ≈ kr ?hGC4 -=1<hGC41jF ( ) titi LL ee E E ωω − +=  >  PQ =H?EC)E=+KCA > >   = r L1F F  ID1W1W?1< EeF  −= LC-]1<c  ( ) EdrV    −= L  P$Q d  =1<++W1jFL E  1<C)1.WD) !G+2h? ( ) rVH I  = C@1/8kc >  == dd LCS <1<:@KCaE:wRCJ 0S+/:a"K1/<+.?? ddd ==  1<F0CK-c ( ) ( )       − − = > > tdE tdE H I  P3Q E5&+,C@+*8k?+2+2C) <Gc       =   ρρ ρρ ρ   P'Q 0C-1EPQ.c  [ ] nmnm H i LL L ρρ   =  P6Q 1.1.2. Các quá trình phân rã x; -.T5.FRE</D?8?l+ -+T)Ea())Ea.Y"#REF 8kC))EI?REUF 5S ?a12]L4uRh : 5YE+,]1@?RH E+,]1@/(1<"# I?REF <"# I?E+ 3 •Quá trình phân rã do phát xạ tự phát yREF1<"#CTE+,] 1@?FC)*RHE+,]1@/p- R./REF5+)CJ:&1<y + <y + Ly  ,1<R./#+/TE+<0C W?CJ12z?1{+Ly + C@RCJ.c                                                kT W m m eCP − =   P+|LQ P9Q }h+, ~ < ~ L•   <•  1<J]1@ ,LC)5.?<#c   A dt dP TN =  P>Q ?C€  1<&.HZ.WL&.H<D)<?8*/ <uRCJC@8kF&+f= γ 1<HC) ? REFLc  R A τ γ    ==  PQ • Phân rã do va chạm UF+T)EaD)S<?CS&21;5 !&,)-"*Y.FKC)51< .F+T)I?E+0RhC-"#E+L<+.5 IE/,EL+,]1@5.O Ca8T4E+<<+ ..OT<a@-:5<+.t 1?Ep-?*E+C5NLK8•".F/D ?ARE.R‚?"#E+ UFE+*T"#"=W?.FCa? E1@L-"*1<CaY+,]1@< .+,]1@LYE<.EX&, I?4E?C@+*8THC) C@+<?+2C)4 ' T+,5?#z1?"=? E+C<lL=HC) 1< coll γ LCE1@<C@8KJW?H C)E+ > v τ ^%_ >  τ γ = coll  PQ p2 coll γγγ += ƒ 1<HC) I?*"#RE< "#E+?&iT&C)/ #HC) I?E+KC@8•" 1.1.3. Tương tác giữa hệ nguyên tử với trường khi tính đến phân rã y#P6Qu1<@1;TuC4C)L <G.H5::1<?<?<C.N<+,]1@ 5&1@.8-?F-*2L I?SL.HK]<]1@ 5&K.8-+)C))a<?CUF+T)CKI? E+LI?.F+T)FLI?.F+T)V?1Wi#2CKa "L4*8a.*T5]<<? #L,1<*C+<?+2.*+, ]L"# 0C#5& IEc [ ] ( ) nmnmnm H i LLL L γρρρ −=    P%Q ?CX1<X+1??<G5LXC@ 8KItaGcs)G+* LGM1ECA?X+1?5 ?GC41jFC&X+1??<GC@8KItc  dEHH −= > L λ1<?+*"#:?I? FLI?E+L ρ 1< ?+2+2C) i+|L|c 6 [ ]       =   L ρρ ρρ ρ H       − −   WdE dEW \       − −   WdE dEW         ρρ ρρ | |        +−− +−−   WdEdEW WdEdEW ρρρρ ρρρρ  \        +−+− −−   ρρρρ ρρρρ WdEWdE dEWdEW |       −−−−−− −+−− QPQPQP QPQPQP   ρρρρρ ρρρρρ dEWWdE WWdEdE L PQ ?C   > WW − = ω 1<G.HK+,5&1@ YC2C@&#?.Hc  QP ρρρρρ Γ+Γ−−=   idE  P$Q   > QP ργρρρωρ −−+=   idE i  P$8Q  > QP ργρρρωρ −−−−=   idE i  P$Q   QP ρρρρ Γ−−−=   idE P$IQ  QP   ρρρρ −=−   dE i  P$WQ Y,4  ρ <  ρ +*R./lE5 ET+,  <  P  ρ <  ρ MC@RW+1<+2C) 45+,,QM  ρ L  ρ +*R./KE +,PC14MC@=1<R./K1jF+) C*1<hK1jFQ (K21@?:?S.LCJ„8-.H+ QP … QLP …  tt ρρ "&,.c ti L ett ω ρρ QP … QP  = L ti L ett ω ρρ − = QP … QP  L P3Q  ti L ti LL eie ωω ρωρρ  …… +=   L ti L ti LL eiett ωω ρωρρ −− −=  … QP … QP    P'Q P'Q<PQ<?&#P$Q C@&#.c 9  ( )  >  Q …… P  ρρρρρ ωωωω Γ+Γ−−+= −− titititi LLLL eeee idE    P6Q   ( ) ( ) tititititi L ti LLLLLL eee idE eieie ωωωωωω ργρρρωρωρ  > > …  ……… −−++=+ −   P68Q  ( ) ( ) tititititi L ti LLLLLL eee idE eieie ωωωωωω ργρρρωρωρ −−−−− −−+−−=−  > > …  ………   P 6Q  ( )( )  >  ……  ρρρρ ωωωω Γ−−+−= −− titititi LLLL eeee idE   P6IQ .      >  Q ………… P  ρρρρρρρ ωω Γ+Γ−+−−= − titi LL ee idE   P9Q  ( ) ( )   > > …   ……… ργρρρωρωρ ω −−+++−= − ti L L e idE ii   P98Q  ( ) ( )   > > …   ……… ργρρρωρωρ ω −−+−−= ti L L e idE ii   P9Q       >  Q ………… P  ρρρρρρ ωω Γ−+−−−= − titi LL ee idE    P9IQ ?hGC4."8•".HEI?C) ti L e ω  < ti L e ω  − LCl.ID:& L ωω −=∆ > =1<C)1&GL  > dE =Ω =1<G.H78L  Γ <  Γ ,1<HC)F F E+,< :C@c   Q …… P  ρρρρρ Γ+Γ−− Ω = i  P>Q ( ) ( )   …… ρρργρ − Ω +∆+−= i i  P>8Q ( ) ( )   …… ρρργρ − Ω −∆−−= i i  P>Q   Q …… P  ρρρρ Γ−− Ω −= i  P>IQ > . Chương 2 ' ĐIỀU KHIỂN SỰ HẤP THỤ VÀ TÁN SẮC TRONG HỆ NGUYÊN TỬ 87 Rb CẤU HÌNH LAMBDA 2.1. Cấu trúc năng lượng của nguyên tử 87 Rb 2.1.1. Cấu trúc tinh. BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC VINH ------------ HOÀNG HỒNG KHUÊ ĐIỀU KHIỂN SỰ HẤP THỤ VÀ TÁN SẮC TRONG HỆ NGUYÊN TỬ 87 Rb CẤU HÌNH LAMBDA Chuyên