Direct probing of quantum phase space by photon counting

We propose a very simple experimental setup to measure, via photoncounting, the overlap of the Wigner functions characterizing two single mode light beams. We show that this scheme can be applied to determine directly the phase space quasiprobability distribution of the single mode field and in a certain limit the Wigner function can be measured with no use of tomographic reconstruction algorithms. Deteriorating effects of nonunit photodetector efficiency are analyzed.

References(29)

Figures(0)

[1]

On the quantum correction for thermodynamic equilibrium

Eugene P. Wigner
(
- Princeton U.
)

- Phys.Rev. 40 (1932) 749-760
•
DOI:
- 10.1103/PhysRev.40.749

[1]

Distribution functions in physics: Fundamentals

M. Hillery
(
- New Mexico U. and
- Munich, Max Planck Inst. Quantenopt.
)
,
R.F. O'Connell
(
- Louisiana State U.
)
,
M.O. Scully
(
- Munich, Max Planck Inst. Quantenopt. and
- New Mexico U.
)
,
Eugene P. Wigner
(
- Louisiana State U.
)

- Phys.Rept. 106 (1984) 121-167
•
DOI:
- 10.1016/0370-1573(84)90160-1

[2]

See for example Lectures on Quantum Optics (Akademie Verlag, Berlin, 1994)

W. Vogel
,
D.-G. Welsch

[3]

K. Vogel
,
H. Risken

- Phys.Rev.A 40 (1989) R2847

[4]

Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum

- Phys.Rev.Lett. 70 (1993) 1244-1247
•
DOI:
- 10.1103/PhysRevLett.70.1244

[4]

D.T. Smithey
,
M. Beck
,
J. Cooper
,
M.G. Raymer
,
A. Faridani

- Phys.Scripta T 48 (1993) 35

[4]

M.G. Raymer
,
J. Cooper
,
H.J. Carmichael
,
M. Beck
,
D.T. Smithey

- J.Opt.Soc.Am.B 12 (1995) 1801

[5]

IEEE J. Quantum Electron QE-20, 803 (1984)

J.H. Shapiro
,
S.S. Wagner

[6]

M. Freyberger
,
W. Schleich

- Phys.Rev.A 47 (1993) R30

[6]

U. Leonhardt
,
H. Paul

- Phys.Rev.A 47 (1993) R2460

[7]

N.G. Walker

- J.Mod.Opt. 34 (1987) 15

[8]

The double homodyne detection has been realized experimentally in the context of phase measurement by

N.G. Walker
,
J.E. Caroll

- Opt.Quant.Electron. 18 (1986) 355

[8]

Measurement of the quantum phase by photon counting

- Phys.Rev.Lett. 67 (1991) 1426-1429
•
DOI:
- 10.1103/PhysRevLett.67.1426

[8]

- Phys.Rev.A 45 (1992) 424

[8]

- Phys.Rev.A 46 (1992) 2840

[9]

Density operators and quasiprobability distributions

Kevin E. Cahill
(
- Harvard U.
)
,
R.J. Glauber
(
- Harvard U.
)

- Phys.Rev. 177 (1969) 1882-1902
•
DOI:
- 10.1103/PhysRev.177.1882

[10]

A. Royer

- Phys.Rev.Lett. 55 (1985) 2745

[10]

Wigner function as the expectation value of a parity operator

Antoine Royer
(
- Unlisted
)

- Phys.Rev.A 15 (1977) 449-450
•
DOI:
- 10.1103/PhysRevA.15.449

[11]

U. Leonhardt

- Phys.Rev.A 48 (1993) 3265

[12]

K. Wódkiewicz

- Phys.Rev.Lett. 52 (1984) 1064

[12]

- Phys.Lett.A 115 (1986) 304

[12]

A124, 207 (1987). For a review see

S. Stenholm

- Annals Phys. 218 (1992) 233

[13]

V. Bužek
,
C.H. Keitel
,
P.L. Knight

- Phys.Rev.A 51 (1995) 2575

[13]

- Phys.Rev.A 51 (1995) 2594

[14]

It has been recently noted ) that the true photon statistics can be recovered from data measured by an imperfect detector, provided that its efficiency is greater than 50%. However, application of this method in calculating Wout(0) turns out to be equivalent to setting s = 1 - η in Eq. (12), which leads to problems discussed in the text

T. Kiss
,
U. Herzog
,
U. Leonhardt

- Phys.Rev.A 52 (1995) 2433

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