Header Page of 89 I HC HU TRNG I HC S PHM NGUYN TH XUN HOI NGHIấN CU CC TNH CHT PHI C IN, Dề TèM AN RI V VIN TI LNG T CA MT S TRNG THI PHI C IN MI LUN N TIN S VT Lí HU, 2016 Footer Page of 89 Header Page of 89 I HC HU TRNG I HC S PHM NGUYN TH XUN HOI NGHIấN CU CC TNH CHT PHI C IN, Dề TèM AN RI V VIN TI LNG T CA MT S TRNG THI PHI C IN MI Chuyờn ngnh: Vt lý lý thuyt v vt lý toỏn Mó s: 62 44 01 03 LUN N TIN S VT Lí Ngi hng dn khoa hc: PGS.TS Nguyn Bỏ n PGS.TS Trng Minh c HU, 2016 Footer Page of 89 Header Page of 89 LI CM N Trờn ng hc tp, nghiờn cu ca mỡnh, tụi ó may mn gp c nhng ngi thy, ngi cụ ỏng kớnh Tụi khụng tỡm c t ng no ngoi li cm n chõn thnh by t lũng bit n cng nh s kớnh trng ca mỡnh i vi nhng gỡ cỏc thy, cụ ó dnh cho tụi Xin chõn thnh cm n thy Trng Minh c, thy khụng nhng l ngi nh hng cho nghiờn cu ca tụi, dy cho tụi cỏch vit mt bi lun nghiờn cu chi tit n tng du chm, du phy t cũn l sinh viờn s phm m cũn l ngi luụn giỳp , ng viờn v c v cho tụi vng tin vt qua nhng khú khn c bit, thy ó gii thiu v mang n cho tụi c hi nhn c s quan tõm v giỳp ca thy Nguyn Bỏ n, mt ngi thy ht lũng vỡ hc trũ Nhng ngy thỏng ngn ngi c lm vic trc tip vi thy tn th ụ Seoul ó cho tụi khụng nhng kin thc, s t tin m cũn l nhng k nim khụng bao gi quờn v tm lũng ca mt ngi thy ó dnh cho mt a hc trũ khụng cú gỡ ni bt nh tụi mt ga tu in nh, thy luụn n trc v i tụi ú mi cui tun tụi c nhn nhng bi ging t thy v thp thm i email tụi bỏo tin ó v n nh an ton sau mi bui hc L cun lun vi chi chớt nhng gúp ý t ni dung n chi tit tng cõu ch L ni lo lng gii thiu tụi cho giỏo s Kisik Kim - i hc Inha m cha bit tụi cú lm thy tht vng hay khụng Xin gi n thy tm lũng tri õn ca ngi hc trũ vi li s tip tc ng ny mt cỏch nghiờm tỳc v cú kt qu Tụi cng xin gi li cm n n thy inh Nh Tho, mc du khụng trc tip hng dn tụi nghiờn cu ny nhng thy luụn quan tõm, giỳp v chia s nim vui vi Footer Page of 89 Header Page of 89 tụi mi tụi cú c hi c hc tp, nghiờn cu nc ngoi, hay tụi t c mt kt qu no ú Kớnh gi n tt c cỏc thy, cụ ó tng ging dy cho tụi lũng bit n sõu sc Trõn trng cm n Khoa Vt lý - Trng i hc S phm - i hc Hu cựng tt cỏc thy, cụ khoa ó giỳp , to mi iu kin thun li cho tụi thi gian nghiờn cu v hon thnh lun ỏn Xin chõn thnh cm n Phũng o to sau i hc - Trng i hc S phm - i hc Hu vi s giỳp nhit tỡnh ca ch Trn Th ụng H vic hon thnh cỏc th tc hnh chớnh sut quỏ trỡnh hc cng nh chun b cho vic bo v lun ỏn Tụi cng xin gi li cm n n cỏc thy, cụ, anh, ch, em ng nghip Khoa Vt lý - Trng i hc S phm - i hc Nng ó luụn giỳp , to diu kin tt nht cho tụi nghiờn cu, hc v cụng tỏc Xin cm n Qu phỏt trin khoa hc v cụng ngh Quc gia ó ti tr kinh phớ cho tụi vic cụng b cỏc cụng trỡnh khoa hc Cui cựng l li cm n n nhng ngi thõn gia ỡnh Cui cựng khụng phi vỡ kộm quan trng m vỡ gia ỡnh luụn l nhng ngi ng sau ng viờn v ht lũng ng h tụi sut quỏ trỡnh hc Cm n b m ó luụn bờn cnh v t ho v Cm n cụ em gỏi ó luụn vui vi nhng nim vui ca ch, ó tn tỡnh giỳp ụng b chm súc nhúc Cafe nhng ngy ch vng nh Cm n chng ó luụn bờn cnh giỳp , ng viờn, ng h v ht mỡnh M cng cm n nhúc Cafe ỏng yờu, ngoan ngoón v yờu quý m sau nhng ngy thỏng khụng bờn m Cm n hai b nhiu lm Xin chõn thnh cm n tt c! Footer Page of 89 Header Page of 89 LI CAM OAN Tụi xin cam oan õy l cụng trỡnh nghiờn cu ca riờng tụi Cỏc kt qu, s liu, th c nờu lun ỏn l trung thc v cha tng c cụng b bt k mt cụng trỡnh no khỏc Tỏc gi lun ỏn Footer Page of 89 Header Page of 89 Kí HIU VIT TT Footer Page of 89 T vit tt Tờn y ting Anh Tờn y ting Vit BS Beam splitter Thit b tỏch chựm DC Downconverter B chuyn i PD Photo-detector Mỏy m photon Header Page of 89 MC LC Trang ph bỡa Li cm n Li cam oan Ký hiu vit tt Mc lc Danh sỏch hỡnh v M u Chng Tng quan v trng thỏi phi c in, tiờu chun dũ tỡm an ri v vin ti lng t 10 1.1 Trng thỏi phi c in 10 1.1.1 Trng thỏi kt hp - nh ngha trng thỏi phi c in 12 1.1.2 Trng thỏi nộn 17 1.1.3 Trng thỏi kt hp thờm photon 19 1.2 Tiờu chun dũ tỡm an ri 21 1.2.1 Phng phỏp nh lng ri 23 Footer Page of 89 Header Page of 89 1.2.2 Tiờu chun an ri Shchukin-Vogel 25 1.3 Vin ti lng t 28 1.3.1 Vin ti lng t vi bin giỏn on 31 1.3.2 Vin ti lng t vi bin liờn tc 35 Chng Trng thỏi nộn dch chuyn thờm photon hai mode 38 2.1 nh ngha trng thỏi nộn dch chuyn thờm photon hai mode 39 2.2 Hm Wigner ca trng thỏi nộn dch chuyn thờm photon hai mode 43 2.3 To trng thỏi nộn dch chuyn thờm photon hai mode 48 2.3.1 S s dng thit b tỏch chựm 49 2.3.2 S s dng b chuyn i tham s khụng suy bin 55 Chng Cỏc tớnh cht phi c in ca trng thỏi nộn dch chuyn thờm photon hai mode 61 3.1 Tớnh cht nộn tng 62 3.2 Tớnh cht nộn hiu 68 3.3 Tớnh cht phn kt chựm 71 3.4 Tớnh cht an ri 77 3.4.1 iu kin an ri 77 3.4.2 Hm phõn b s photon 80 Footer Page of 89 Header Page of 89 3.4.3 nh lng ri 84 Chng Vin ti lng t s dng ngun ri nộn dch chuyn thờm photon hai mode 88 4.1 Biu thc gii tớch ca tin cy trung bỡnh 89 4.2 Tớnh s v bin lun 94 Kt lun 99 Danh mc cụng trỡnh khoa hc ca tỏc gi ó s dng lun ỏn103 Ti liu tham kho 104 Ph lc 116 Footer Page of 89 Header Page 10 of 89 DANH SCH HèNH V 1.1 S ph thuc ca h s nộn Sx ca trng thỏi kt hp thờm photon vo tham s dch chuyn || vi cỏc giỏ tr ca m = 0, 5, 10, 20 20 1.2 S ph thuc ca h s Q ca trng thỏi kt hp thờm photon vo tham s dch chuyn || vi cỏc giỏ tr ca m = 0, 5, 10, 20 20 2.1 S ph thuc ca hm G(||) vo || cho m, n tha iu kin (a) m + n = v (b) m + n = 48 2.2 S to trng thỏi nộn dch chuyn thờm photon hai mode s dng thit b tỏch chựm 50 2.3 S ph thuc ca tin cy F FBS v xỏc sut thnh cụng tng ng P PBS vo h s truyn qua t ca cỏc thit b tỏch chựm BS1 v BS2 = = s = 0.1 vi {m, n} = {1, 1}, {1, 2} v {2, 2} 53 2.4 S ph thuc ca tin cy F FBS v xỏc sut thnh cụng tng ng P PBS vo h s truyn qua t ca cỏc thit b tỏch chựm BS1 v BS2 m = n = vi = = s = 0.1, 0.3 v 0.5 Footer Page 10 of 89 54 Header Page 126 of 89 112 [64] Lee C T (1991), Measure of the nonclassicality of nonclassical states, Physical Review A, 44(5), pp R2777-1 - R2777-4 [65] Lee C T (1991), Theorem on nonclassical states, Physical Review A, 52(4), pp R2775-1 - R2775-3 [66] Lee C T (1990), Higher-order criteria for nonclassical effects in photon statistics, Physical Review A, 41, pp 1721 - 1723 [67] Lee C T (1990), Many photon antibunching in generalized pair coherent states, Physical Review A, 41, pp 1569 - 1575 [68] Levenson M D et all (1985), Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber Physical Review A, 32, pp 1550 - 1562 [69] Mandel L (1982), Squeezed States and Sub-Poissonian Photon Statistics, Physical Review Letter, 49, pp 136 - 138 [70] Milburn G J., Braunstein S L (1999), Quantum teleportation with squeezed vacuum states, Physical Review A, 60, pp 937-941 [71] Manko O V (1997), Symplectic tomography of nonlinear coherent states of a trapped ion, Physics Letters A, 228, pp 29 - 35 [72] Nielsen M A (1999), Conditions for a class of entanglement transformations, Physics Review Letters, 83, pp 436 - 439 [73] Nielsen M A and Chuang I L (2000), Quantum Computation and Quantum information, Cambridge University Press [74] Pathak A and Garcia M E (2006), Control of higher-order antibunching, Applied Physics B, 84, pp 479 - 484 Footer Page 126 of 89 Header Page 127 of 89 113 [75] Parker S., Bose S and Plenio M B (2000), Entanglement quantification and purification in continuous-variable systems, Physics Review A, 61, pp 032305-1 - 032305-4 [76] Peres A (1996), Separability criterion for density matrices, Physical Review Letters, 77(8), pp 1413 - 1415 [77] Puri R R (2001), Mathematical methods of quantum optics, Berlin: Springer [78] Roy B and Roy P (1999), Phase properties of even and odd nonlinear coherent states, Physics Letters A, 257, pp 264 - 268 [79] Schrăodinger E (1935), Die gegenwăartige Situation in der Quantenmechanik, Naturwissenschaften, 23(49), pp 807 812 (The present situation in quantum mechanics, hyperlink "https://en.wikipedia.org/wiki/Naturwissenschaften") [80] Shchukin E., Vogel W (2005), Inseparability criterion for continuous bipartite quantum states, Physical Review Letters, 95(23), pp 230502-1 - 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662 Footer Page 129 of 89 Header Page 130 of 89 116 PH LC A Chng minh biu thc A1 Chng minh biu thc (2.33) chng minh biu thc (2.33), ta cn s dng tớch phõn c bit [21] n i d2 zi zT exp (z z M T z 1/2 = (detM ) + (à exp (à uT ) T u )M àT T , (A.1) ú M = A B C D v C D M = A B (A.2) vi A, B, C, D l cỏc ma trn n ì n chiu v z z1 , z2 , zn chng minh cụng thc (2.33) Tớnh phõn cn tớnh l d2 ua d2 ub TP = exp d2 ua d2 ub = exp (ua àa + ub àb ua àa ub àb ) ì exp ua ub ei + ua ub ei r |ua |2 + |ub |2 (A.3) Footer Page 130 of 89 Header Page 131 of 89 117 vi = 1/2 So sỏnh cỏc i s ca hm exp phng trỡnh A.3 vi uT (u u ) M T u uT + (à v ) T , u ta cú uT (u u ) M T u = ua ub ei + ua ub ei r |ua |2 + |ub |2 (A.4) v (à uT v) T u = ua àa + ub àb ua àa ub àb (à uT à) T (A.5) u Vi trng thỏi hai mode, (u u )M uT uT = (ua ub ua = (ua ub ua B12 u a B22 ub D12 ua ub D22 A A B11 11 12 A A22 B21 21 ub ) C11 C12 D11 C21 C22 D21 A u + A12 ub + B11 ua + B12 ub 11 a A u + A22 ub + B21 ua + B22 ub 21 a ub ) C11 ua + C12 ub + D11 ua + D12 ub C21 ua + C22 ub + D21 ua + D22 ub = (A12 + A21 ) ua ub + (D12 + D21 ) ua ub + (B11 + C11 ) ua ua + (B22 + C22 ) ub ub = ua ub ei + ua ub ei r + |ua |2 + |ub |2 Footer Page 131 of 89 Header Page 132 of 89 118 Suy A12 = A21 = ei r, D = D = ei r, 12 21 B11 = C11 = , B22 = C22 = , (A.6) hay i e i e r M = r i e r i e r 0 (A.7) Vỡ vy M = 0 i e ei r v M a b2 aa = b b2 aa ú a = ei r, b = i e r e r 0 r a b2 aa b b2 aa 0 0 b b2 aa a b2 aa i (A.8) , a b2 aa b b2 aa (A.9) Suy det M = b4 2b2 |a|2 + |a|4 = b2 |a|2 Footer Page 132 of 89 (A.10) Header Page 133 of 89 119 v (à à) M àT àT a b2 aa b b2 aa àa 0 a b b2 aa 0 b2 aa àb = (àa àb àa àb ) b a b2 aa 0 b2 aa àa b a àb b2 aa b2 aa b a b2 aa àb b2 aa àa a b b a b aa b aa = (àa àb àa àb ) b a b2 aa àa + b2 aa àb b a b2 aa àb + b2 aa àa a b a b à à à àb àb a a b a a b b aa b aa b aa b aa b a b a à à à àa àb a a b b a b b aa b2 aa b2 aa b2 aa 2a 2b 2b 2a = à à àb àb a b a a b a b aa b aa b aa b aa = Vi = 1/2 thỡ b = nờn det M = (1 tanh2 r) = (cosh r)4 (A.11) v (à )M àT T = 2(|àa |2 + |àb |2 ) cosh2 r 2(àa àb ei + àa àb ei ) sinh r cosh r (A.12) Thay hai biu thc ny vo (A.1) ta c phng trỡnh (2.33) TP = cosh2 r exp (|àa |2 + |àb |2 ) cosh2 r (àa àb ei + àa àb ei ) sinh r cosh r (A.13) Footer Page 133 of 89 Header Page 134 of 89 120 PH LC B Chng trỡnh tớnh s B1 tin cy FBS v xỏc sut thnh cụng PBS ca trng thỏi to thnh s s dng thit b tỏch chựm (H s chun húa = Cmn, Xỏc sut thnh cụng = P, tin cy = F) Clear[F\[CapitalDelta], Cmn, Frac, Nmn, P, F]; F\[CapitalDelta][\[CapitalDelta]_Integer, m_Integer, n_Integer, i_Integer, j_Integer, s_, a_, b_] := (a^(2 (m - j) - \[CapitalDelta]) b^(2 (n - i) - \[CapitalDelta]) m! n! Hypergeometric2F1[1 + i + \[CapitalDelta], + j + \[CapitalDelta], + \[CapitalDelta], Tanh[s]^2] (-Tanh[s])^\[CapitalDelta])/((-j + m - \[CapitalDelta])! (-i + n - \[CapitalDelta])! \[CapitalDelta]!); Frac[m_Integer, n_Integer, i_Integer, j_Integer] := (m! n!)/ (j! (m - j)! i! (n - i)!); Cmn[m_Integer, n_Integer, s_, a_, b_] := (1/(Cosh[s])^2) \!(\*UnderoverscriptBox[(\[Sum]), (j = 0), (m)] (\*UnderoverscriptBox[(\[Sum]), (i = 0), (n)]((Frac[m, n, i, j] ((\*UnderoverscriptBox[(\[Sum]), (\[CapitalDelta] = 0), (Min[m - j, n - i])] 2\F\[CapitalDelta][\[CapitalDelta], m, n, i, j, s, a, b] F\[CapitalDelta][0, m, n, i, j, s, a, b])))))); Nmn[m_Integer, n_Integer, s_, a_, b_] := 1/Sqrt[Cmn[m, n, s, a, b]]; P[h_Integer, m_Integer, n_Integer, s_, a_, b_, t_] := (t^-2 - 1)^(m + n)/(t^4 m! n!) \!(\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] Footer Page 134 of 89 Header Page 135 of 89 121 (\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] ((FractionBox[SuperscriptBox[((1 -\*SuperscriptBox[(t), (-2)])), (l + k)], ((l!) (k!))] Cmn[m + l, n + k, s, a, b])))); F[h_Integer, m_Integer, n_Integer, s_, a_, b_, t_] := ((Nmn[m, n, s, a, b])^2 (\!(\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] ((FractionBox[SuperscriptBox[((1 -\*SuperscriptBox[(t), (-1)])), (l + k)], ((l!) (k!))] Cmn[m + l, n + k, s, a, b])))))^2) /(\!(\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] ((FractionBox[SuperscriptBox[((1 - \*SuperscriptBox[(t), (-2)])), (l + k)], ((l!) (k!))] Cmn[m + l, n + k, s, a, b]))))); B2 tin cy FDC v xỏc sut thnh cụng PDC ca trng thỏi to thnh s s dng b chuyn i tham s (Xỏc sut thnh cụng = PDC, tin cy = FDC) PDC[h_Integer, m_Integer, n_Integer, s_, a_, b_, z_] := (Sinh[z])^(2 (m + n))/(m! n!) \!(\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] ((FractionBox[SuperscriptBox[((1 -\*SuperscriptBox[((Cosh[z])), (2)])),(l + k)],((l!)(k!))] Cmn[m + l, n + k, s, a, b])))); FDC[h_Integer, m_Integer, n_Integer, s_, a_, b_, z_] := ((Nmn[m, n, s, a, b])^2 (\!(\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] ((FractionBox[SuperscriptBox[((1-Cosh[z])),(l + k)],((l!)(k!))] Cmn[m + l, n + k, s, a, b])))))^2) /\!(\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] ((FractionBox[SuperscriptBox[((1 - \*SuperscriptBox[((Cosh[z])), (2)])),(l + k)],((l!)(k!))] Cmn[m + l, n + k, s, a, b])))); B3 H s nộn tng S Clear[m, r, a, b, x, y]; Footer Page 135 of 89 Header Page 136 of 89 122 sh := Sinh[r]; ch := Cosh[r]; T[m_, r_, a_, b_, x_, y_] := 2*(m + 1)*(m + 2)*Cos[2*x]*sh^2*ch^2*LaguerreL[m, -a^2*(Sech[r])^2] 4*(m + 2)*Cos[x + y]*sh*ch*a*b*LaguerreL[m, 1, -a^2*(Sech[r])^2] + 2*Cos[2*y]*a^2*b^2*LaguerreL[m, 2, -a^2*(Sech[r])^2] 4*((m + 1)*Cos[x]*sh*ch*LaguerreL[m, -a^2*(Sech[r])^2] Cos[y]*a*b*LaguerreL[m, 1, -a^2*(Sech[r])^2])^2/ LaguerreL[m, -a^2*(Sech[r])^2] + 2*(m + 1)*ch^2*(sh^2 + b^2)*LaguerreL[m + 1, -a^2*(Sech[r])^2] + 2*(m + 1)^2*sh^2*ch^2*LaguerreL[m, -a^2*(Sech[r])^2] 2*(sh^2 + b^2)*LaguerreL[m, -a^2*(Sech[r])^2] 2*m*sh^2*LaguerreL[m - 1, -a^2*(Sech[r])^2] 4*(m + 1)*Cos[x - y]*sh*ch*a*b*LaguerreL[m, 1, -a^2*(Sech[r])^2] + 4*Cos[x - y]*Tanh[r]*a*b*LaguerreL[m - 1, 1, -a^2*(Sech[r])^2]; M[m_, r_, a_, b_, x_, y_] := (m + 1)*ch^2* LaguerreL[m + 1, -a^2*(Sech[r])^2] + (sh^2 + b^2)* LaguerreL[m, -a^2*(Sech[r])^2] + m*sh^2*LaguerreL[m - 1, -a^2*(Sech[r])^2] 2*Cos[x - y]*Tanh[r]*a*b*LaguerreL[m - 1, 1, -a^2*(Sech[r])^2]; S[m_, r_, a_, b_, x_, y_] := T[m, r, a, b, x, y]/M[m, r, a, b, x, y]; B4 H s nộn hiu D Clear[m, r, a, b, x, y, T, M, D]; T[m_, r_, a_, b_, x_, y_] := 2*Cos[2*x]*Tanh[r]^2*a^4*LaguerreL[m - 2, 4, -a^2*(Sech[r])^2] -4* Cos[x + y]*Tanh[r]*a^3*b*LaguerreL[m - 1, 3, -a^2*(Sech[r])^2] +2* Cos[2*y]*a^2*b^2*LaguerreL[m, 2, -a^2*(Sech[r])^2] +(m + 1)* Cosh[r]^2*(2*(Cosh[r]^2 + b^2) - 1)* LaguerreL[m + 1, -a^2*(Sech[r])^2] +(2*(m + 1)^2*Sinh[r]^2*Cosh[r]^2 Cosh[r]^2 - b^2)*LaguerreL[m, -a^2*(Sech[r])^2] -m*Sinh[r]^2* LaguerreL[m - 1, -a^2*(Sech[r])^2] -2*Cos[x - y]*a*b*(2*(m + 1)*Sinh[r]* Cosh[r]*LaguerreL[m, 1, -a^2*(Sech[r])^2] - Tanh[r]* LaguerreL[m - 1, 1, -a^2*(Sech[r])^2]) -(4*(Cos[x]*Tanh[r]*a^2* LaguerreL[m - 1, 2, -a^2*(Sech[r])^2] - Cos[y]*a*b* LaguerreL[m, 1, -a^2*(Sech[r])^2])^2)/ LaguerreL[m, -a^2*(Sech[r])^2]; Footer Page 136 of 89 Header Page 137 of 89 123 M[m_, r_, a_, b_, x_, y_] := \[Sqrt]((m + 1)*Cosh[r]^2* LaguerreL[m + 1, -a^2*(Sech[r])^2] - (Cosh[r]^2 + b^2)* LaguerreL[m,-a^2*(Sech[r])^2]-m*Sinh[r]^2*LaguerreL[m-1,-a^2*(Sech[r])^2] +2*Cos[x - y]*Tanh[r]*a*b*LaguerreL[m - 1, 1, -a^2*(Sech[r])^2])^2; D[m_, r_, a_, b_, x_, y_] := T[m, r, a, b, x, y]/M[m, r, a, b, x, y] - 1; B5 H s phn kt chựm Rlk Clear[m, n, s, a, b, i, j, l, k, Clvkt, Nlk, Rlk]; Clvkt[m_Integer, n_Integer, l_Integer, v_Integer, k_Integer, t_Integer, s_, a_, b_, \[CurlyPhi]_] := \*UnderoverscriptBox[(\[Sum]), (j = 0), (m + l)] (\*UnderoverscriptBox[(\[Sum]), (p = 0), (m + v)] (\*UnderoverscriptBox[(\[Sum]), (q = 0), (p)] (\*UnderoverscriptBox[(\[Sum]), (jj = 0), (n + t)] (\*UnderoverscriptBox[(\[Sum]), (pp = 0), (n + k)] (\*UnderoverscriptBox[(\[Sum]), (qq = 0), (pp)] ((m + l)!(m + v)!(n + t)!(n + k)! SuperscriptBox[(Cosh[s]), (2 ((j + jj)) - q - qq)] SuperscriptBox[(((-Sinh[s]))), (q + qq)] SuperscriptBox[(a), (m + l - j + p - q)] SuperscriptBox[(b), (n + t - jj + pp - qq)] Exp[I\\[CurlyPhi](qq - q)] KroneckerDelta[j, m + v - p + qq] KroneckerDelta[jj, n + k - pp + q])/((m + l - j)!(m + v - p)!(p - q)! q!(n + t - jj)!(n + k - pp)!(pp - qq)!(qq)!)))))); Nlk[l_Integer, k_Integer, m_Integer, n_Integer, s_, a_, b_,\[CurlyPhi]_]:= \*UnderoverscriptBox[(\[Sum]), (i = 0), (l)] (\*UnderoverscriptBox[(\[Sum]), (j = 0), (k)] ((SuperscriptBox[(((-1))), (i + j)]\*SuperscriptBox[(l!), (2)] SuperscriptBox[(k!), (2)] Clvkt[m + l - i, n + k - j, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]))/(i!j! SuperscriptBox[(((l - i))!), (2)] \*SuperscriptBox[(((k - j))!), (2)])); Rlk[l_Integer, k_Integer, m_Integer, n_Integer, s_, a_, b_,\[CurlyPhi]_]:= 1/(Nlk[l, k, m, n, s, a, b, \[CurlyPhi]] + Nlk[k, l, m, n, s, a, b,\[CurlyPhi]]) (Nlk[l + 1, k - 1, m, n, s, a, b,\[CurlyPhi]] + Nlk[l - 1, k + 1, m, n, s, a, b, \[CurlyPhi]]) - 1; Footer Page 137 of 89 Header Page 138 of 89 124 B6 H s an ri E E[m_Integer, n_Integer, s_, a_, b_, \[CurlyPhi]_] := (Clvkt[m, n, 1, 1, 0, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]] - Clvkt[m, n, 0, 1, 0, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]* Clvkt[m, n, 1, 0, 0, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]) (Clvkt[m, n, 0, 0, 1, 1, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]] - Clvkt[m, n, 0, 0, 0, 1, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]* Clvkt[m, n, 0, 0, 1, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]) (Clvkt[m, n, 0, 1, 0, 1, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]] Clvkt[m, n, 0, 1, 0, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]* Clvkt[m, n, 0, 0, 0, 1, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]) (Clvkt[m, n, 1, 0, 1, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]] Clvkt[m, n, 1, 0, 0, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]* Clvkt[m, n, 0, 0, 1, 0, s, a, b, \[CurlyPhi]]/ Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]); (a) B7 Hm phõn b s photon Pq Paqq[K_Integer, m_Integer, n_Integer, q_Integer, s_, a_, b_] := E^-a^2/(Cosh[s]^2 Cmn[m, n, s, a, b]) \!( \*UnderoverscriptBox[(\[Sum]), (k = 0), (K)] (\*UnderoverscriptBox[(\[Sum]), (kk = 0), (K)] (\*UnderoverscriptBox[(\[Sum]), (i = 0), (n)] (\*UnderoverscriptBox[(\[Sum]), (ii = 0), (n)] (\*UnderoverscriptBox[(\[Sum]), (l = 0), (q)] Footer Page 138 of 89 Header Page 139 of 89 125 (\*UnderoverscriptBox[(\[Sum]), (ll = 0), (q)] (\*UnderoverscriptBox[(\[Sum]), (t = 0), (m)] (\*UnderoverscriptBox[(\[Sum]), (tt = 0), (m)] ((SuperscriptBox[(n!), (2)] (k + i)!) (k + t)! (kk + tt)! q! SuperscriptBox[(m!), (2)]))/ (i!(n - i)! (ii)! (n - ii)! k! (kk)! l! (q - l)! (ll)! (q - ll)!) (SuperscriptBox[(-1), (t + tt - l - ll)] SuperscriptBox[(a), (2 q - l + k + kk - ll + m)] SuperscriptBox[(b), (2 n - i - ii)] SuperscriptBox[(Tanh[s]), (k + kk)] KroneckerDelta[kk + ii, k + i])/ (t! (m - t)! (tt)! (m - tt)! (k + t - l)! (kk + tt - ll)!))))))))); B8 Entropy tuyn tớnh L Co[n_Integer, k_Integer, kk_Integer, x_] := \! \*UnderoverscriptBox[(\[Sum]), (i = 0), (n)] (\*UnderoverscriptBox[(\[Sum]), (j = 0), (n)] ((\*FractionBox[((n!) (n!) (((k + i))!) SuperscriptBox[(x), (2 n - i - j)] KroneckerDelta[k + i,kk + j]), (i! (n - i)! j! (n - j)! \*SqrtBox[k! (kk)!)])])))); L[h_Integer, m_Integer, n_Integer, s_, a_, b_] := - \!(\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (kk = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (l = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (ll = 0), (h)](( FractionBox[SuperscriptBox[(((-Tanh[s]))),(k + kk + l + ll)], (SuperscriptBox[(Cosh[s]),4]\*SuperscriptBox[Cmn[m, n, s, a, b],2])] Co[m, kk, ll, a] Co[m, l, k, a] Co[n, k, kk, b] Co[n, ll, l, b])))))); B9 tin cy trung bỡnh Fav ca quỏ trỡnh vin ti trng thỏi kt hp Fav[h_Integer, m_Integer, n_Integer, s_, a_, b_, \[CurlyPhi]_] := 1/(Cosh[s]^2 Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]) \!(\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (kk = 0), (h)] \*FractionBox[SuperscriptBox[((Tanh[s])), (k + kk)] (n + m + k + kk))!, k! (kk)! 2^(m + n + k + kk + 1))])); Footer Page 139 of 89 Header Page 140 of 89 126 B10 tin cy trung bỡnh Fav ca quỏ trỡnh vin ti trng thỏi Fock FavOP[h_Integer, m_Integer, n_Integer, t_Integer, s_, a_,b_,\[CurlyPhi]_] :=1/(Cosh[s]^2 Clvkt[m, n, 0, 0, 0, 0, s, a, b, \[CurlyPhi]]) \!(\*UnderoverscriptBox[(\[Sum]), (k = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (kk = 0), (h)] (\*UnderoverscriptBox[(\[Sum]), (p = 0), (Min[m + k, t])] (\*UnderoverscriptBox[(\[Sum]), (pp = 0), (Min[m + kk, t])] (\*UnderoverscriptBox[(\[Sum]), (q = 0), (Min[n + k, t])] (\*UnderoverscriptBox[(\[Sum]), (qq = 0), (Min[n + kk, t])] ((SuperscriptBox[((Tanh[s])),(k + kk)]SuperscriptBox[-1,p+pp+q+qq] (m + k)!(m + kk)!(n + k)!(n + kk)!(m+n+k+kk+2t-p-pp-q-qq)!t!^2)/ (k!(kk)!p!(pp)!q!(qq)!(m + k - p)!(m + kk - pp)!(n + k - q)! (n + kk - qq)!(t - p)!(t - pp)!(t - q)!(t - qq)! SuperscriptBox[2, m + n + k + kk + Footer Page 140 of 89 t + - p - pp - q - qq])))))))); ... nguồn phi cổ điển mạnh Đó lý chọn đề tài "Nghiên cứu tính chất phi cổ điển, dò tìm đan rối viễn tải lượng tử số trạng thái phi cổ điển mới" Các trạng thái phi cổ điển mà muốn khảo sát lớp trạng thái. .. TỔNG QUAN VỀ TRẠNG THÁI PHI CỔ ĐIỂN, TIÊU CHUẨN DÒ TÌM ĐAN RỐI VÀ VIỄN TẢI LƯỢNG TỬ 1.1 Trạng thái phi cổ điển Các trạng thái phi cổ điển trạng thái có nhiều ứng dụng quan trọng vật lý chất rắn,... NGUYỄN THỊ XUÂN HOÀI NGHIÊN CỨU CÁC TÍNH CHẤT PHI CỔ ĐIỂN, DÒ TÌM ĐAN RỐI VÀ VIỄN TẢI LƯỢNG TỬ CỦA MỘT SỐ TRẠNG THÁI PHI CỔ ĐIỂN MỚI Chuyên ngành: Vật lý lý thuyết vật lý toán Mã số: 62 44 01 03 LUẬN