???

1
??????????????(BEC)???????? ??????????????????
?
????(????)
?????

• ?????(???) ????(???)
• ????(????) ???(???)

??????? 2008?5?23?
2
??

• ?????????????(????)
• ?????????????
• ??????????????(BEC)
• BEC?????????
• ????????????
• ???

3
1. Introduction
4
????????????
????

• ?? ???????????? ? ????

WMAP???CMB
?1
??????????????? ? ????????
???????????????? ? Hawking ??
?2
???????????????????????????
5
Hawking ??
Introduction

• ??????????????????????????
• ?????????????????????(Hawking ??)
• ??????? (Hawking ??)

( ?????????????????)
???????
?????????????????????????????????????? ???????????
??????????(Hawking ??)???????
6
Hawking ??
Introduction

• ?????????????? Hawking ???????????

???? Hawking ??
????
?????????
??????????????????????????????
CMB???????????!
???????????????????????????
7
?????
Introduction
Unruh PRL (1981)

• ?????????????????(??)??????
• ???????????????????
• ??????????????????????????????????????????
• ? ?????????????????????????!

8
??????????
Classical

• ?????????????????????????????????????.
• (0) ??????????????? ??horizon????.
• (1)
• (2) ???????horizon??? ??????.
• ???????????? Hawking ??
• 
  

Quantum
?????????????
??????????!
9
????????1
????? ??????
????????
???????? Klein-Gordon ???????????????? ??????
Klein-Gordon ??
????????? ???
????????????
10
????????2

?????
??????????????
??????
???????
????????????????

???????? number op.????? ???????
? ?????????????
11
????????3
??????????????????
Bogoliubov coefficients
??????
Number op.
??????????????????!
12
2.?????
13
???????????
analogy
Unruh PRL (1981)

• ??????(???)
• ?????????

???
????
??
??(???)???????????????????????????
14
???????????
analogy

• ?????????????????????(??)???.
• ??????(??) ? ????? ??????????.

??
??(???)
???(???)
???(????)
???????????????????????
????????????????? ??????????????????
15
?????????
analogy

• ???????????????
• ????????
• ????????????
• ???????????????
• ??????????
• ??????????????
• ????????????????? horizon ???????

Sonic horizon
?????????
16
Unruh (1981)
analogy
Assumption for the state

• ??????????????????????????????????????????????????
  ????????????????????????.
• ??????????

???!
??????????
??????????? ??????
BEC?????!
17
3. Bose-Einstein ???(BEC)
18
???? Bose-Einstein ???
BEC

• ????????????????????????
• ?????????????????????????????????????????????? ?
  ??
• 1995???????????????????????????????????????

????????????? ????? ????? 1nK???? ???????
400nK, 200nK, 50nK
19
Gross-Pitaevskii ???
BEC
?????? ?????
?????????????????
??????????????????
Trapping potential
Atomic interaction
????
????
???????
???
???????????????
20
Gross-Pitaevskii ???
BEC
?????? ?????
?????????????????
??????????????????
Trapping potential
Atomic interaction
????
????
???????
???
???????????????
??????????
????????????????????????
21
BEC?????
BEC

• BEC???????Bogoliubov-de Gennes (BdG) ??????.
• BdG???

??????
????????????
??
?????????????????????
22
Bogoliubov?????????

• ?????????????????????????

???????????????! ??????????????? ???????????????
Bogoliubov ???
23
4. Analogy in BEC
24
Bogoliubov????????
Analogy in BEC

• ?????????? Bogoliubov ??????????
• ???????????????????????????????

???????
Gross-Pitaevskii ???
???
?????
Bogoliubov-de Gennes (BdG) ???
??
???????
??
?????????????!
25
Bogoliubov ????????2
Analogy in BEC

• ??????Bogoliubov ???????????? respect ????

??????????Klein-Gordon ?????????????!
???????
Bogoliubov ????????????????????????? (???????????
??)
26
Bogoliubov ????????2
Analogy in BEC

• ??????Bogoliubov ???????????? respect ????

• ?BEC??????? ?????????????
• (???????????????????)
• ????????????.
• (BdG??? ? ??????????????)
• ???????QFT?????????????????
• (??????????????)

??????????Klein-Gordon ?????????????!
Bogoliubov ????????????????????????? (???????????
??)
27
BEC??????
Analogy in BEC

• ??????????????????
• ?????????????

Bogoliubov ??
initial
final
28
Analogy in BEC
?????????????
???

B-dG?????????????
dynamical evolution
????
?????????????
???? ? ?????? ? ????
???
????? Klein-Gordon ??
29
5.???????????
30
?????

• ????BEC???
• ? ????(?????)???.
• ?????????????????????????.
• ??????????BEC???????????????
• ?????
• ??BEC??????????????????????!.

Kurita, Morinari PRA 76 (2007) 053603
31
???????????
?????????????? (?????BEC)
(1) who whoi ????????? (2) t 0 ???? whof
0.707 whoi ???BEC?????
??????????????87Rb????BEC
????????
32
??BEC?????????
Kurita, Morinari PRA 76 (2007) 053603
???????
(1)???who whoi ? ?????????? ??????? (2) t
0 ???? whof 0.707 whoi ??? BEC?????
???????
??
33
????(??????)
????????(????)?????? ????????????????
preliminary
??
?????????????? 1.4 nK ???
34
Hawking ??

• Hawking?????(???????????)

BEC???????????????????
???????
???????(???)???????????
35
????????????
preliminary
36
????????????
Hawking ?????
preliminary
37
???1

• ???????????????????????????????????????????
• ????????????????? ? BEC???
• BEC??????????????????????????(BEC????????????!)

38
???2

• BEC??? ? ????(?????)???.
• ???????QFT??????????????
• ????????????????????.
• ??????????????Bogoliubov????????????????.
• ? BdG????????????????????.
• ??????????????????????????
• ??????????????????????????Hawking?????????.

?????
39
??

• ??BEC??????????????????????????????????
• BEC?????Hawking ????????????????????????????????
  (??????????????)
• ???????????????

40
?????
????? ??????????????????????-??????
(?????????????) ??4?????-????
1?????????? ?????1024 ???? Dx 0.0625????
Dt 110-8
???????????????????2048??????????????????????????1
024?????????????1024??????????????????????????????
?2048????????
?????????????????
41
Case 1 ???????
analogy

• ?????????
• ?????????

)
)
)
??(????????)? ???
??( )??????????????
sound velocity
2???????
????????????
?????????
42
Case 2 ???????
analogy

• ?(??)???????????

)
)
)
??(????????)????
horizon
?????????
43
????????
preliminary

• BEC ?????????????
• ?????????????????
• ?????????????
• ??????
• ???????? BEC????
• ????????????????
• ????????????????
• ??????
• ???????????????
• ?????????

??????????????????? ???????????????????????????
44
??????BEC
???????
(1)???who whoi ? ?????????? ??????? (2) t
0 ???? ? ??????????? ???? whof 0.707
whoi ???