I HC HU

TRNG I HC S PHM

NGUYN TH XUN HOI

NGHIN CU CC TNH CHT PHI C IN,

D TM AN RI V VIN TI LNG T

CA MT S TRNG THI PHI C IN MI

LUN N TIN S VT L

HU, 2016

I HC HU

TRNG I HC S PHM

NGUYN TH XUN HOI

NGHIN CU CC TNH CHT PHI C IN,

D TM AN RI V VIN TI LNG T

CA MT S TRNG THI PHI C IN MI

Chuyn ngnh: Vt l l thuyt v vt l ton

M s: 62 44 01 03

LUN N TIN S VT L

Ngi hng dn khoa hc:

1. PGS.TS. Nguyn B n 2. PGS.TS. Trng Minh c

HU, 2016

LI CM N

Trn con ng hc tp, nghin cu ca mnh, ti may mn gp

c nhng ngi thy, ngi c ng knh. Ti khng tm c t ng

no ngoi li cm n chn thnh by t lng bit n cng nh s knh

trng ca mnh i vi nhng g cc thy, c dnh cho ti. Xin chn

thnh cm n thy Trng Minh c, thy khng nhng l ngi nh

hng cho nghin cu ca ti, dy cho ti cch vit mt bi lun nghin

cu chi tit n tng du chm, du phy t khi cn l sinh vin s

phm m cn l ngi lun gip , ng vin v c v cho ti vng tin

vt qua nhng kh khn. c bit, thy gii thiu v mang n cho

ti c hi nhn c s quan tm v gip ca thy Nguyn B n,

mt ngi thy ht lng v hc tr. Nhng ngy thng ngn ngi c

lm vic trc tip vi thy tn th Seoul cho ti khng nhng kin

thc, s t tin m cn l nhng k nim khng bao gi qun v tm

lng ca mt ngi thy dnh cho mt a hc tr khng c g ni

bt nh ti. mt ga tu in nh, thy lun n trc v i ti

mi cui tun ti c nhn nhng bi ging t thy v thp thm

i email ti bo tin v n nh an ton sau mi bui hc. L cun

lun vn vi chi cht nhng gp t ni dung n chi tit tng cu ch.

L ni lo lng khi gii thiu ti cho gio s Kisik Kim - i hc Inha

khi m cha bit ti c lm thy tht vng hay khng. Xin gi n thy

tm lng tri n ca ngi hc tr vi li ha s tip tc con ng ny

mt cch nghim tc v c kt qu. Ti cng xin gi li cm n n thy

inh Nh Tho, mc du khng trc tip hng dn ti trong nghin

cu ny nhng thy vn lun quan tm, gip v chia s nim vui vi

ti mi khi ti c c hi c hc tp, nghin cu nc ngoi, hay khi

ti t c mt kt qu no . Knh gi n tt c cc thy, c

tng ging dy cho ti lng bit n su sc.

Trn trng cm n Khoa Vt l - Trng i hc S phm - i

hc Hu cng tt cc thy, c trong khoa gip , to mi iu kin

thun li cho ti trong thi gian nghin cu v hon thnh lun n.

Xin chn thnh cm n Phng o to sau i hc - Trng i

hc S phm - i hc Hu vi s gip nhit tnh ca ch Trn Th

ng H trong vic hon thnh cc th tc hnh chnh trong sut qu

trnh hc tp cng nh chun b cho vic bo v lun n.

Ti cng xin gi li cm n n cc thy, c, anh, ch, em ng

nghip trong Khoa Vt l - Trng i hc S phm - i hc Nng

lun gip , to diu kin tt nht cho ti trong nghin cu, hc

tp v cng tc.

Xin cm n Qu pht trin khoa hc v cng ngh Quc gia ti

tr kinh ph cho ti trong vic cng b cc cng trnh khoa hc.

Cui cng l li cm n n nhng ngi thn trong gia nh. Cui

cng khng phi v km quan trng m v gia nh lun l nhng ngi

ng sau ng vin v ht lng ng h ti trong sut qu trnh hc tp.

Cm n b m lun bn cnh v t ho v con. Cm n c em gi

lun vui vi nhng nim vui ca ch, tn tnh gip ng b chm sc

nhc Cafe nhng ngy ch vng nh. Cm n chng lun bn cnh

gip , ng vin, ng h v ht mnh. M cng cm n nhc Cafe

ng yu, ngoan ngon v vn yu qu m sau nhng ngy thng khng

bn m. Cm n hai b con nhiu lm.

Xin chn thnh cm n tt c!

LI CAM OAN

Ti xin cam oan y l cng trnh nghin cu ca ring ti. Cc

kt qu, s liu, th c nu trong lun n l trung thc v cha

tng c ai cng b trong bt k mt cng trnh no khc.

Tc gi lun n

K HIU VIT TT

T vit tt Tn y ting Anh Tn y ting Vit

BS Beam splitter Thit b tch chm

DC Downconverter B chuyn i

PD Photo-detector My m photon

MC LC

Trang ph ba

Li cm n

Li cam oan

K hiu vit tt

Mc lc

Danh sch hnh v

M u 1

Chng 1. Tng quan v trng thi phi c in, tiu chun

d tm an ri v vin ti lng t 10

1.1. Trng thi phi c in . . . . . . . . . . . . . . . . . . . 10

1.1.1. Trng thi kt hp - nh ngha trng thi phi c

in . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.1.2. Trng thi nn . . . . . . . . . . . . . . . . . . . 17

1.1.3. Trng thi kt hp thm photon . . . . . . . . . . 19

1.2. Tiu chun d tm an ri . . . . . . . . . . . . . . . . . 21

1.2.1. Phng php nh lng ri . . . . . . . . . . 23

1.2.2. Tiu chun an ri Shchukin-Vogel . . . . . . . . 25

1.3. Vin ti lng t . . . . . . . . . . . . . . . . . . . . . . 28

1.3.1. Vin ti lng t vi bin gin on . . . . . . . 31

1.3.2. Vin ti lng t vi bin lin tc . . . . . . . . . 35

Chng 2. Trng thi nn dch chuyn thm photon hai

mode 38

2.1. nh ngha trng thi nn dch chuyn thm photon hai

mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2. Hm Wigner ca trng thi nn dch chuyn thm photon

hai mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.3. To trng thi nn dch chuyn thm photon hai mode . 48

2.3.1. S s dng thit b tch chm . . . . . . . . . 49

2.3.2. S s dng b chuyn i tham s khng suy

bin . . . . . . . . . . . . . . . . . . . . . . . . . 55

Chng 3. Cc tnh cht phi c in ca trng thi nn dch

chuyn thm photon hai mode 61

3.1. Tnh cht nn tng . . . . . . . . . . . . . . . . . . . . . 62

3.2. Tnh cht nn hiu . . . . . . . . . . . . . . . . . . . . . 68

3.3. Tnh cht phn kt chm . . . . . . . . . . . . . . . . . . 71

3.4. Tnh cht an ri . . . . . . . . . . . . . . . . . . . . . . 77

3.4.1. iu kin an ri . . . . . . . . . . . . . . . . . . 77

3.4.2. Hm phn b s photon . . . . . . . . . . . . . . 80

3.4.3. nh lng ri . . . . . . . . . . . . . . . . . . 84

Chng 4. Vin ti lng t s dng ngun ri nn dch

chuyn thm photon hai mode 88

4.1. Biu thc gii tch ca tin cy trung bnh . . . . . . . 89

4.2. Tnh s v bin lun . . . . . . . . . . . . . . . . . . . . 94

Kt lun 99

Danh mc cng trnh khoa hc ca tc gi s dng trong lun n103

Ti liu tham kho . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Ph lc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

DANH SCH HNH V

1.1. S ph thuc ca h s nn Sx ca trng thi kt hp

thm photon vo tham s dch chuyn || vi cc gi tr

ca m = 0, 5, 10, 20 . . . . . . . . . . . . . . . . . . . . 20

1.2. S ph thuc ca h s Q ca trng thi kt hp thm

photon vo tham s dch chuyn || vi cc gi tr ca

m = 0, 5, 10, 20 . . . . . . . . . . . . . . . . . . . . . . . 20

2.1. S ph thuc ca hm G(||) vo || cho m, n tha mn

iu kin (a) m+ n = 3 v (b) m+ n = 6 . . . . . . . . 48

2.2. S to trng thi nn dch chuyn thm photon hai

mode s dng thit b tch chm . . . . . . . . . . . . . 50

2.3. S ph thuc ca tin cy F FBS v xc sut thnh

cng tng ng P PBS vo h s truyn qua t ca cc

thit b tch chm BS1 v BS2 khi = = 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 xc sut thnh

cng tng ng P PBS vo h s truyn qua t ca

cc thit b tch chm BS1 v BS2 khi m = n = 1 vi

= = s = 0.1, 0.3 v 0.5 . . . . . . . . . . . . . . . . . 54

2.5. S to trng thi nn dch chuyn thm photon hai

mode s dng b chuyn i tham s khng suy bin . . 56

2.6. S ph thuc ca tin cy F FDC v xc sut thnh

cng tng ng P PDC vo tham s nn z ca DC2 v

DC3 khi = = s = 0.1 vi {m,n} = {1, 1}, {1, 2} v

{2, 2} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

2.7. S ph thuc ca tin cy F FDC v xc sut thnh

cng tng ng P PDC vo tham s nn z ca DC2 v

DC3 khi m = n = 1 vi = = s = 0.1, 0.3 v 0.5 . . . 58

3.1. S ph thuc ca h s nn tng S vo cc gc 1 v 2

khi || = 2, || = 5 v r = 0.5 cho trng hp thm mt

photon vo mode a (m = 1, n = 0) . . . . . . . . . . . . 65

3.2. S ph thuc ca h s nn tng S vo gc 2 khi c nh

1 = 0 vi || = 2, || = 5 v r = 0.5 cho {m,n} = {1, 0},

{5, 0} v {10, 0} . . . . . . . . . . . . . . . . . . . . . . . 65

3.3. S ph thuc ca h s nn tng S vo cc tham s

dch chuyn c hai mode || v || khi 1 = 2 = 0,

r = 0.35 cho trng hp ch thm mt photon vo mode

a (m = 1, n = 0) . . . . . . . . . . . . . . . . . . . . . . 66

3.4. S ph thuc ca h s nn tng S vo tham s dch

chuyn (a) || (khi c nh || = 20); (b) || (khi c nh

|| = 5) vi 1 = 2 = 0, r = 0.5 cho {m,n} = {1, 0},

{5, 0} v {10, 0} . . . . . . . . . . . . . . . . . . . . . . . 67

3.5. S ph thuc ca h s nn tng S vo tham s nn r

khi 1 = 2 = 0, || = 2.5, || = 5 cho {m,n} = {1, 0},

{5, 0} v {10, 0} . . . . . . . . . . . . . . . . . . . . . . . 67

3.6. S ph thuc ca h s nn hiu D vo cc gc 1 v 2

khi || = 2, || = 5 v r = 0.5 cho trng hp ch thm

mt photon vo mode a (m = 1, n = 0) . . . . . . . . . . 70

3.7. S ph thuc ca h s nn hiu D vo tham s dch

chuyn (a) || (khi c nh || = 10); (b) || (khi c nh

|| = 2) vi 1 = 2 = 0, r = 0.5 cho {m,n} = {1, 0},

{5, 0} v {10, 0} . . . . . . . . . . . . . . . . . . . . . . . 70

3.8. S ph thuc ca h s nn hiu D vo tham s nn r

khi 1 = 2 = 0, || = 2 v || = 10 cho {m,n} = {1, 0},

{5, 0} v {10, 0} . . . . . . . . . . . . . . . . . . . . . . . 70

3.9. S ph thuc ca cc h s phn kt chm R11, R31 v

R52 vo gc khi || = 0.1, || = 0.7, r = 0.8 cho trng

hp m = 3, n = 0 . . . . . . . . . . . . . . . . . . . . . . 74

3.10. S ph thuc ca h s phn kt chm (a) R11 v (b) R42

vo tham s nn r khi || = 0.1, || = 0.7 v = cho

{m,n} = {2, 0}, {4, 0} v {6, 0} . . . . . . . . . . . . . . 74

3.11. S ph thuc ca h s phn kt chm Rlk vo tham s

nn r vi || = 0.1, || = 0.7 v = cho m = 1, n = 0

khi (a) k = 3, l thay i t 3 n 6, (b) l = 4, k thay i

t 1 n 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.12. S ph thuc ca cc h s phn kt chm Rlk (gm R66,

R54, R42 v R52) vo tham s nn r vi || = 0.1, || = 0.7

v = cho m = 3, n = 0 . . . . . . . . . . . . . . . . . 75

3.13. S ph thuc ca h s phn kt chm (a) R11 v (b)

R22 vo tham s nn r vi || = || = 0.2 v = cho

{m,n} = {3, 3}, {3, 4}, {3, 1} v {3, 0} . . . . . . . . . . 75

3.14. S ph thuc ca h s an ri E vo gc vi {a, b} =

{0, 0}, {0, /2} v {0, } khi c nh cc tham s cn li

ti || = || = 0.1, r = 1 v m = n = 1 . . . . . . . . . . 78

3.15. S ph thuc ca h s an ri E vo tham s nn r vi

|| = || = 0.1, a = b = 0 v = cho {m,n} = {0, 0},

{1, 0}, {1, 1}, {2, 1} v {2, 2} . . . . . . . . . . . . . . . . 78

3.16. Hm phn b s photon P(a)q cho mode a khi c nh

tham s nn s = 1 ca (a) trng thi nn hai mode, (b)

trng thi nn thm photon hai mode vi {m,n} = {1, 1}

v (c) trng thi nn dch chuyn thm photon hai mode

vi {m,n} = {1, 1}, = = 0.5 . . . . . . . . . . . . . . 83

3.17. Entropy tuyn tnh L ca trng thi nn hai mode, trng

thi nn thm photon hai mode vi mt photon c thm

vo mi mode {m,n} = {1, 1} v trng thi nn dch

chuyn thm photon hai mode vi = = 0.5 v lng

photon thm vo cng l {m,n} = {1, 1} theo tham s

nn r khi c nh = . . . . . . . . . . . . . . . . . . 86

3.18. S ph thuc ca entropy tuyn tnh L ca trng thi

nn dch chuyn thm photon hai mode vo tham s nn

r vi = v = = 0.1 cho {m,n} = {0, 0}, {1, 0},

{1, 1}, {2, 1} v {2, 2} . . . . . . . . . . . . . . . . . . . 87

4.1. S ph thuc ca tin cy trung bnh Fav ca qu

trnh vin ti trng thi kt hp | s dng ngun ri

nn dch chuyn thm photon hai mode vo tham s nn

r vi = v = = 0 cho {m,n} = {3, 3}, {3, 2},

{3, 1} v {3, 0} . . . . . . . . . . . . . . . . . . . . . . . 95

4.2. S ph thuc ca tin cy trung bnh Fav ca qu

trnh vin ti trng thi Fock |1 s dng ngun ri nn

dch chuyn thm photon hai mode vo tham s nn r vi

= v = = 0 cho {m,n} = {3, 3}, {3, 2}, {3, 1} v

{3, 0} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.3. S ph thuc ca tin cy trung bnh Fav ca qu

trnh vin ti trng thi kt hp v trng thi Fock |1 s

dng ngun ri nn dch chuyn thm photon hai mode

vo tham s nn r vi = , = = 0 cho {m,n} = {1, 1} 97

4.4. S ph thuc ca tin cy trung bnh Fav ca qu

trnh vin ti trng thi Fock |2 s dng ngun ri nn

hai mode v ngun ri nn dch chuyn thm photon hai

mode cho {m,n} = {1, 1}, {2, 2} v {3, 3} vo tham s

nn r vi = v = = 0 . . . . . . . . . . . . . . . 97

1

M U

1. L do chn ti

Thng tin lin lc lun l nhu cu tt yu ca con ngi trong mi

thi i. Cng vi s pht trin ca khoa hc k thut, lnh vc thng

tin lin lc khng ngng pht trin c v phng tin v cch thc truyn

tin m bo thng tin c truyn i xa, nhanh, chnh xc v bo

mt. Trong cng ngh truyn tin quang hc, cc nh khoa hc lun c

s quan tm c bit n vic tm cch gim thiu ti a cc tp m hay

cc thng ging lng t trong qu trnh truyn tin bi chnh cc thng

ging ny lm cho tn hiu b nhiu, gim chnh xc ng thi ko

theo gim c tc truyn tin. Trn thc t, cc nh vt l l thuyt ln

thc nghim tip cn ti gii hn lng t chun v ngy cng tin

xa hn tm ra cc trng thi vt l m cc thng ging lng

t c hn ch n mc ti a, mang li s ci thin ng k v tnh

lc la, chnh xc v c bit l tnh bo mt ca thng tin truyn

i [35]. Tuy nhin, vi cch thc truyn thng tin m chng ta vn ang

s dng hin nay th tnh bo mt ca thng tin khng c m bo.

u thng tin vn c th lt ra ngoi d c m ha rt nhiu

ln. Vy liu c cch no thng tin truyn i xa m vn m bo

cht lng v bo mt mt cch tuyt i? Cu tr li nm trong mt

l thuyt mi c xut gn y l thuyt thng tin lng t m

2

thng tin khng nhng c m ha trong cc trng thi lng t

m cn c x l theo cc quy lut ca c hc lng t [31].

L thuyt thng tin lng t l s kt hp gia c hc lng t

v l thuyt thng tin. Vi nhng tnh cht c bit ca h lng t,

khi c p dng vo cc qu trnh x l thng tin s cho ta nhng

iu k diu vt ln hn nhng qu trnh x l thng tin c in ti

u nht. V d, nu thng tin c m ha trong trng thi lng t

th tnh khng th copy ca trng thi lng t s m bo cho thng

tin c bo mt. T khi ra i, l thuyt thng tin lng t khng

ngng pht trin v hin vn ang thu ht s ch ca nhiu nh khoa

hc k c l thuyt v thc nghim trn ton th gii, trong vin ti

lng t c xem nh l mt trong nhng qu trnh ni bt nht [31],

[47]. Mt cch ngn gn, vin ti lng t l qu trnh m thng tin c

th c chuyn i vi chnh xc v tnh bo mt tuyt i nh s

dng mt h lng t c bit (c gi l h an ri hon ho) kt

hp vi mt knh thng tin c in. Trong qu trnh ny, thng tin c

chuyn n ngi nhn bng cch hy trng thi mang thng tin ni

gi ri khi phc n ni nhn thng qua trng thi an ri c

chia s trc m khng cn truyn trc tip trng thi mang thng

tin. Nh thng tin hon ton c bo mt. Vin ti lng t c

a ra ln u tin bi Bennett v cc cng s trong phm vi bin ri

rc [24] v sau cng c xut vi bin lin tc bi Vaidman

[93]. tng ca Vaidman tip tc c m t mt cch gn vi thc

nghim hn bi Braunstein v Kimble [30]. Li th ca vin ti lng

t s dng h bin lin tc l c th truyn tin bng sng in t. Tuy

nhin, vn gp phi i vi bin lin tc l m bo tin cy

ca qu trnh vin ti bng mt (ngha l thng tin c chuyn i vi

3

chnh xc tuyt i) cn phi c mt ngun ri hon ho. Trong m

hnh ca Braunstein v Kimble, ngun ri c xut l trng thi

nn hai mode. Trng thi ny l trng thi l tng vi iu kin tham

s nn ca n l v cng. Tht khng may, iu l tng bao gi cng

ch nm trong cc bn tho l thuyt. Trn thc t, trng thi nn hai

mode to c bng thc nghim c mc nn (trong trng hp ny

cng chnh l ri) tng i nh, ko theo tin cy ca qu trnh

vin ti khng cao. Thc t ny, kt hp vi nhiu vn thc nghim

khc lm cho qu trnh vin ti mc d c tin hnh thnh cng

trong phng th nghim nhng tin cy t c cng ch mi 0.58

[28], [45], [89]. Do vy, tm ra gii php cho cc kh khn lin quan n

hin thc ha vin ti lng t, m trc hn ht l vic tm ngun ri

v ci thin ri ca n trong iu kin thc t, l nhng vn ht

sc quan trng, ang rt c quan tm hin nay bi ngun ri hon

ho l iu kin tin quyt cho s thnh cng ca vin ti ni ring cng

nh bt k mt qu trnh x l thng tin lng t ni chung.

Gn y, trong cc nghin cu v trng thi phi c in ni ln mt

trng thi ng c quan tm, l trng thi kt hp thm photon

[17]. Nh chng ta bit, trng thi kt hp l trng thi c in. Tuy

nhin, sau khi chu tc dng ca ton t sinh photon, n tr thnh mt

trng thi hon ton mi v c hnh thc v tnh cht. Cc hiu ng phi

c in nh hiu ng nn v sub-Poisson bt u xut hin bng vic

thm vo trng thi kt hp ch mt photon, cch din t cho vic tc

dng ton t sinh photon ln trng thi mt ln duy nht. Nu tip tc

lp li thao tc ny th cc hiu ng phi c in trn s th hin cng

r [17]. Hn na, theo php o phi c in c xut bi Lee [64],

tc dng ca ton t sinh photon khng ch ln trng thi kt hp m

4

ln bt k mt trng thi no s bin trng thi thnh phi c in

vi phi c in ti a [65]. iu ny gi ra mt hy vng rng vic

tc dng ton t sinh photon ln mt trng thi phi c in c th lm

tng mc ca cc hiu ng phi c in trong c hiu ng an ri.

c bit, m phng thc nghim cho tc dng ca ton t sinh photon

ln trng thi kt hp c tin hnh thnh cng ch vi cc thit b

quang hc thng dng nh thit b tch chm hay b chuyn i tham

s khng suy bin, kt hp vi my m photon [95]. Nh vy, nu thc

s cc hiu ng phi c in, c bit hiu ng an ri, ca trng thi

nn hai mode c tng cng nh tc dng ca ton t sinh photon th

trng thi mi ny ha hn nhng ng dng y kh quan khng nhng

trong lnh vc thng tin lng t m cn trong nhiu lnh vc khc, l

nhng lnh vc i hi mt ngun phi c in mnh. l l do chng

ti chn ti "Nghin cu cc tnh cht phi c in, d tm

an ri v vin ti lng t ca mt s trng thi phi c in

mi". Cc trng thi phi c in mi m chng ti mun kho st y

chnh l lp trng thi c tn trng thi nn dch chuyn thm photon

hai mode, c to thnh bng cch tc dng ton t sinh photon vi

s ln lp li khc nhau v ton t dch chuyn ln trng thi nn hai

mode. Nh nhng g mong i, ti ch ra c rng trng thi nn

dch chuyn thm photon hai mode c phi c in mnh hn v

ri c tng cng so vi trng thi nn thng thng. T xut

mt phng php c ngha thc tin ci thin ri, l tc dng

mt hoc nhiu ln ton t sinh photon vo c hai mode ca trng thi

c ri hu hn cho trc.

5

2. Mc tiu nghin cu

Mc tiu chnh ca ti l kho st vai tr ca ton t sinh photon

i vi cc tnh cht phi c in ca trng thi nn dch chuyn thm

photon hai mode v nh gi hiu sut ca n khi p dng vo qu trnh

vin ti lng t. Mc tiu ny c trin khai thnh cc mc tiu c

th nh sau:

Tm hm Wigner, mt hm phn b gi xc sut, ca trng thi

nn dch chuyn thm photon hai mode cng nh iu kin ca mt s

hiu ng phi c in th hin trong trng thi ny bao gm nn a mode

v phn kt chm bc cao nhm chng t nh hng tt ca ton t

sinh photon ln tnh cht phi c in ca trng thi.

Tm iu kin an ri ca trng thi nn dch chuyn thm photon

hai mode, trn c s chng minh vai tr ca ton t sinh photon trong

vic tng cng ri ca trng thi.

Xc nh tin cy trung bnh ca qu trnh vin ti lng t

khi s dng ngun ri l trng thi nn dch chuyn thm photon hai

mode v chng t tc dng tch cc ca trng thi ny trong vic ci

thin tin cy vin ti.

a ra cc s thc nghim thm photon vo trng thi nn

dch chuyn hai mode v kho st chi tit mi lin h gia tin cy

ca trng thi to c v xc sut thnh cng.

6

3. Ni dung nghin cu v phm vi nghin cu

Vi mc tiu ra nh trn, ti tp trung vo ba ni dung

chnh:

Nghin cu chung v trng thi nn dch chuyn thm photon hai

mode bao gm xc nh h s chun ha trong trng hp tng qut khi

thm photon vo c hai mode v tnh hm Wigner ca trng thi.

Kho st cc s to trng thi nn dch chuyn thm photon

hai mode da trn cc thit b quang hc thng dng nh thit b tch

chm, b chuyn i tham s v my m photon.

Nghin cu mt s tnh cht phi c in ca trng thi nn dch

chuyn thm photon hai mode nh tnh cht nn tng, nn hiu, phn

kt chm bc cao v c bit l tnh cht an ri.

Kho st tin cy trung bnh ca qu trnh vin ti lng t s

dng ngun ri l trng thi nn dch chuyn thm photon hai mode.

Tt c cc nghin cu u bao gm tm biu thc gii tch ca cc

h s c trng cho vn ang xem xt ri tnh s cc kt qu gii

tch ny, trn c s a ra cc nhn xt v bin lun cn thit. Do

tnh phc tp trong qu trnh a ra cc biu thc gii tch cng nh

khi tnh s m mt s nghin cu ch kho st vi cc tham s thc,

ngha l cho pha phc ca n bng khng. iu ny s c nhc n

cng nh gii thch c th trong phn ni dung ca lun n mi ln

s dng gii hn ny.

7

4. Phng php nghin cu

a ra biu thc gii tch ca cc h s c trng cho cc hiu

ng phi c in, hiu ng an ri, tin cy vin ti cng nh hm

Wigner, chng ti s dng hai phng php nghin cu l thuyt c

th trong quang lng t v thng tin lng t l phng php l thuyt

lng t ha trng ln th hai v phng php thng k lng t. Bn

cnh , bin lun cc kt qu gii tch thu c, trn c s nh

gi vai tr ca ton t sinh photon, chng ti s dng phng php tnh

s bng phn mm chuyn dng Mathematica.

5. ngha khoa hc v thc tin ca ti

Nhng kt qu thu c ca ti ng gp mt phn quan trng

vo n lc tm kim ngun ri mi v ci thin ri ca n c th

s dng cho cc qu trnh vin ti lng t vi bin lin tc trong thc

t. xut c phng php ci thin ri, t gp phn pht

trin l thuyt thng tin lng t. Ngoi ra, kt qu ca ti cn c

vai tr nh hng, cung cp thng tin cho vt l thc nghim trong vic

d tm cc hiu ng phi c in, to ra cc trng thi phi c in v s

dng chng vo qu trnh vin ti lng t.

6. Cu trc ca lun n

Ngoi cc phn m u, kt lun, danh mc cc hnh v, danh mc

cc cng trnh ca tc gi c s dng trong lun n, ti liu tham

kho v ph lc, ni dung ca lun n c trnh by trong 4 chng.

8

Ni dung c th ca cc chng nh sau:

Chng 1 trnh by tng quan v cc nghin cu lin quan n

trng thi phi c in, d tm an ri v qu trnh vin ti lng t

ng thi tm tt mt s c s l thuyt lin quan trc tip n nhng

ni dung nghin cu ca ti nh trng thi kt hp, trng thi nn,

trng thi kt hp thm photon, phng php nh lng ri, tiu

chun an ri Shchukin-Vogel v m hnh vin ti lng t.

Chng 2 trnh by nhng nghin cu chung v trng thi nn

dch chuyn thm photon hai mode bao gm xc nh h s chun ha,

tnh hm phn b gi xc sut Wigner, gii thch v nhn xt hai s

khc nhau to trng thi nn dch chuyn thm photon hai mode.

Chng 3 trnh by nhng nghin cu v cc tnh cht phi c in

ca trng thi nn dch chuyn thm photon hai mode bao gm a ra

cc biu thc gii tch v h s nn tng, h s nn hiu, h s phn

kt chm, h s an ri, hm phn b s photon v entropy tuyn tnh;

xem xt s ph thuc ca cc h s ny vo cc tham s ca trng thi

cng nh s photon c thm vo ri rt ra nhng nhn xt, bin lun

tng ng.

Chng 4 trnh by nghin cu v qu trnh vin ti lng t s

dng ngun ri nn dch chuyn thm photon hai mode bao gm tnh

ton tin cy trung bnh khi vin ti trng thi kt hp hoc trng

thi Fock v kho st nh hng ca tham s nn ca trng thi cng

nh s photon thm vo ln tin cy vin ti.

Cc kt qu nghin cu ca lun n c cng b trong 04 cng

trnh di dng cc bi bo khoa hc, trong c 01 bi ng trong

tp ch chuyn ngnh quc gia (Communications in Physics), 02 bi

9

ng trn tp ch chuyn ngnh quc t nm trong h thng SCI (01

bi trong International Journal of Theoretical Physics, 01 bi trong In-

ternational Journal of Modern Physics B) v 01 bi ng trn tp ch

chuyn ngnh quc t nm trong h thng SCIE (Advances in Natural

Sciences: Nanoscience and Nanotechnology).

10

Chng 1

TNG QUAN V TRNG THI PHI

C IN, TIU CHUN D TM AN

RI V VIN TI LNG T

1.1 Trng thi phi c in

Cc trng thi phi c in l cc trng thi c rt nhiu ng dng

quan trng trong vt l cht rn, quang hc phi tuyn, quang hc lng

t v c bit trong thng tin lng t [1]. T im xut pht ban u

[48] cho n nay, rt nhiu trng thi phi c in khc nhau c

xut v mt l thuyt cng nh c kim chng bng thc nghim.

Trong s c th k n ba lp trng thi m ng dng ca chng

c ghi nhn cng nh chng minh c nhiu tim nng trong tng lai.

Lp trng thi u tin phi k n l trng thi nn. tng

v trng thi nn c Stoler a ra vo nm 1970, l nhng trng

thi m thng ging ca mt i lng no c th nh hn gi tr

tng ng ca trng thi bt nh cc tiu i xng [86], [87]. Mi lm

nm sau, trng thi nn photon c quan st ln u tin trong phng

th nghim bi Slusher [83] v sau c khng nh bi Kimble [63],

11

Levenson v cc cng s [68]. Cc hiu ng nn c m rng theo nhiu

kiu khc nhau chng hn nh nn bin trc giao, nn s ht pha.

Trong nn bin trc giao li c th chia thnh nn bc thp thng

thng hoc nn bc cao theo kiu Hillery [50] hay kiu Hong-Mandel

[56], nn n mode hay nn a mode di dng nn tng [12], [51] v

nn hiu [13], [14], [51]. Hn na, trng thi nn khng ch tn ti vi

photon m cn c pht trin vi cc chun ht khc nh polariton

[19], phonon [85], exciton [2], [5], [10], [11], biexiton [6], [91], [92], v

thm ch trong nguyn t nh nn spin [15]. c bit, khi pht trin ln

cho trng hp hai mode, trng thi nn c chng minh l trng thi

an ri v c s dng trong cc m hnh vin ti lng t cho

tin cy tuyt i trong iu kin l tng [31].

Lp trng thi phi c in tip theo l trng thi kt hp cp [16],

trng thi kt hp chn v l [34]. V sau chng c pht trin thnh

cc trng thi kt hp phi tuyn vi rt nhiu hiu ng phi c in ha

hn mang n nhiu ng dng khc nhau. C th k tn mt s trng

thi quan trng thuc lp ny l trng thi kt hp phi tuyn chn v l

[71], [78], trng thi kt hp phi tuyn K ht [1], [7], trng thi ci qut

[1], [8] v trng thi kt hp b ba [9]. Nu nh trng thi ci qut c

vai tr nh mt trng thi nn a hng th trng thi kt hp b ba li

l mt trng thi ri 3 mode v cng l mt ngun ri quan trng cho

cc ng dng trong lnh vc thng tin lng t v tnh ton lng t.

Lp trng thi phi c in th ba cng c tm quan trng khng

km l cc trng thi c to thnh bng cch tc dng ton t sinh

photon ln mt trng thi quan tm no , c gi l cc trng thi

thm photon. Trng thi thm photon c Agarwal v Tara a ra

vo nm 1991 [17] v gn y c Zavatta xc minh bng thc nghim

12

[95]. K thut thm photon l mt trong nhng k thut to trng thi

rt quan trng c th to ra mt trng thi mong mun bt k [61].

Hn na, cc trng thi thm photon l nhng trng thi th hin nhiu

hiu ng phi c in khc nhau cho d trng thi gc ban u trc khi

c thm photon c th l trng thi c in nh trng thi kt hp

[17]. iu gi cho ta ngh n vic thm photon vo trng thi phi c

in, chng hn nh nn hai mode, c th gia tng cc hiu ng phi c

in ca chng trong c c hiu ng an ri. Nu ng nh nhng g

mong i th lp trng thi ny s c tm quan trng trong vic ci tin

cht lng ca cc qu trnh vin ti lng t bi n c th lm tng

ri ca ngun ri c thm photon. y l mi quan tm chnh ca

chng ti trong nghin cu ny v s c trnh by c th trong cc

chng sau ca lun n. y, trong khun kh ca phn tng quan,

chng ti trnh by s lc mt s trng thi phi c in lin quan trc

tip n trng thi ca chng ti nh trng thi nn v trng thi kt

hp thm photon. Nhng trc ht, c ci nhn tng quan v khi

nim trng thi phi c in, chng ti gii thiu ngn gn v trng thi

kt hp nh l ranh gii gia c in v phi c in.

1.1.1 Trng thi kt hp - nh ngha trng thi phi c in

Trng thi kt hp, k hiu |, c Glauber [48] v Sudarshan

[88] a ra vo nm 1963 m t cc tnh cht ca chm sng laser.

l trng thi ring ca ton t hy photon

a| = |, (1.1)

trong l mt s phc, = ||eia, c gi l tham s dch chuyn

vi bin || bin thin t 0 n v pha a nm trong khong t 0

13

n 2 [rad]. Trong h c s Fock, trng thi kt hp c dng [46]

| = exp(1

2||2)

n=0

nn!|n, (1.2)

trong n l s nguyn khng m. V phng din ton hc, trng thi

kt hp c to thnh bng cch tc dng ton t dch chuyn [46]

D() = exp(a a) (1.3)

ln trng thi chn khng nh sau:

| = D()|0. (1.4)

Trng thi kt hp mc du l trng thi c in nhng cc tnh

cht ca n u nm gii hn cui cng cn c th c chp nhn

theo quan im c in. Do nh sng kt hp c xem l ranh gii

gia nh sng c in v phi c in. iu kin cn v ng vi ranh

gii ny da trn c im ca hm Glauber-Sudarshan P () [49], [88].

Hm P () ca trng thi l h s khai trin ca trng thi trong biu

din trng thi kt hp

=

P ()||d2 (1.5)

tha mn iu kinP ()d2 = 1. Nh vy hm P () c tnh cht

tng t nh hm phn b xc sut. Tuy nhin, P () li c th nhn

gi tr m hoc c tnh k d mnh hn tnh k d ca hm Delta nn

nhn chung khng th c hiu nh mt hm phn b c in v v

vy P () c gi l hm phn b gi xc sut. Trng thi m hm

P () ca n c tnh cht nh mt hm phn b thng k thng thng

c gi l trng thi c in. Tri li, trng thi c hm P () m

hoc k d cao c nh ngha l trng thi phi c in. C th minh

ha cho nh ngha ny bng cch xem xt hm P () ca trng thi

14

nhit (tiu biu cho trng thi c in), trng thi kt hp (ranh gii

gia trng thi c in v phi c in) v trng thi s ht (i din

cho trng thi phi c in). Trng thi nhit c hm P () dng Gauss

P () = (1/n) exp(||2n) [82], trong n l s ht trung bnh. y

l mt hm phn b c in tiu biu, trong khi , vi trng thi kt

hp |0, hm P () l hm Delta (2)( 0). D dng suy ra t tnh

cht ca hm Delta rng y l gii hn cui cng ca mt hm phn

b c in, v v vy, mt hm c xem l k d cao nu tnh k d ca

n mnh hn tnh k d ca hm Delta, chng hn hm P () ca trng

thi s ht |n [82]

P () =e||

2

n!

2n

nn(2)(). (1.6)

Bn cnh hm Glauber-Sudarshan P (), trng thi phi c in i

khi cng c xc nh trn c s ca hm Wigner [22]

W () =2

Tr[D()D()(1)n]. (1.7)

Mc du khng c tnh k d nh hm P () nhng hm Wigner vn c

th nhn nhng gi tr m nn hm Wigner cng l mt hm phn b

gi xc sut. Ni cch khc, tnh m ca hm Wigner cng c th c

dng xc nhn mt trng thi no l phi c in vi lu y ch

l tiu chun . C th, mt trng thi c hm phn b Wigner m th

chc chn l trng thi phi c in. Tuy nhin, iu ngc li khng

phi bao gi cng ng, ngha l mt trng thi phi c in khng nht

thit phi c hm Wigner m. l v c nhng trng thi m hm

P () c th nhn gi tr m - tc l trng thi phi c in - nhng li

s hu hm Wigner lun khng m, chng hn trng thi nn [46].

Ngoi tiu ch da trn hm P () nh va cp trn, ta cng

c th nhn bit cc trng thi c in qua vic xem xt cc tnh cht

15

c th ca n. Theo cch ny th mt trng thi c gi l phi c in

khi n th hin mt hoc nhiu tnh cht phi c in chng hn nh

tnh thng k sub-Poisson, tnh cht phn kt chm, tnh cht nn,...

Cc tnh cht phi c in l nhng tnh cht khng th suy ra t quan

im c in v c xut da trn gii hn m trng thi kt hp

t c.

Khi xem xt tnh thng k photon, trng thi kt hp c chng

minh tun theo phn b Poisson, ngha l trung bnh ca ton t s ht

trong trng thi kt hp s bng phng sai ca n. Nu xem y l

ranh gii th n s chia cc trng thi thnh hai nhm, mt nhm tun

theo thng k super-Poisson vi phng sai ca ton t s ht ln hn

trung bnh ca n v nhm cn li tun theo thng k sub-Poisson vi

tnh cht hon ton ngc li. Nh vy nu t tham s

Q =n2 n2

n, (1.8)

trong n l ton t s ht, th trng thi tun theo thng k super-

Poisson s c Q > 1 v ngc li cho trng hp sub-Poisson. Nhng

trng thi mang tnh thng k sub-Poisson, ngha l c tham s Q < 1,

s hu hm P () m nn chng l cc trng thi phi c in. V vy,

hiu ng sub-Poisson l mt trong nhng tnh cht phi c in c

dng nhn bit cc trng thi phi c in.

Ta cng c th phn bit trng thi phi c in vi c in qua c

im ca hm tng quan bc hai c nh ngha [46]

g(2)() =E()(t)E()(t+ )E(+)(t+ )E(+)(t)E()(t)E(+)(t)E()(t+ )E(+)(t+ )

, (1.9)

trong E()(t) v E(+)(t) tng ng l thnh phn tn s m v thnh

phn tn s dng ca trng ti thi im t. Hm tng quan bc hai

16

ny cung cp cho ta thng tin v xc sut quan st mt cp photon sao

cho mt photon c quan st thi im t th photon kia c quan st

thi im sau mt khong ti cng mt v tr. Vi trng thi kt

hp g(2)() = g(2)(0) = 1 ngha l cc photon xut hin c lp vi nhau.

Nu hai photon c xu hng xut hin theo chm, tc g(2)(0) > g(2)(),

th c gi l photon kt chm. Ngc li nu hai photon c xu hng

ngy cng xut hin ring l, tc g(2)(0) < g(2)(), th c gi l photon

phn kt chm. Vi trng c in, g(2)(0) g(2)() [46]. Do , trng

thi th hin tnh phn kt chm l trng thi phi c in. tin cho

vic p dng vo cc trng thi quang lng t, iu kin tn ti hai

photon phn kt chm g(2)(0) < g(2)() c th c vit li di dng

cc ton t s ht nh sau [66]:

N (2) N2 < 0, (1.10)

trong N = aa v N (i) N(N 1). . . (N i+ 1) = aiai.

Bn cnh hai tnh cht va k trn, trng thi phi c in cn c

th s hu mt tnh cht quan trng - tnh cht nn - da trn vic xem

xt thng ging lng t ca mt bin ng lc no . Xt hai ton

t A v B tha mn h thc giao hon [A, B] = iC. Hai ton t ny

tun theo h thc bt nh Heisenberg

A2B2 14|C|2, (1.11)

trong X2 l k hiu cho phng sai ca ton t X v c xc nh

bi X2 = X2 X2. Mt trng thi no nu tha mn

A2