I= QUANTUM STATE TOMOGRAPHY THROUGH PHASE-SENSITIVE AMPLIFICATION
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Title of Thesis
QUANTUM STATE TOMOGRAPHY THROUGH PHASE-SENSITIVE AMPLIFICATION

Author(s)
Mashhood Ahmad
Institute/University/Department Details
Department of Electronics/ Quaid-i-Azam University, Islamabad
Session
2004
Subject
Electronics
Number of Pages
101
Keywords (Extracted from title, table of contents and abstract of thesis)
quantum state tomography, phase sensitive amplification, tomographic reconstruction, correlated emission laser, balanced homodyne detector, wigner distribution, schrodinger-cat state

Abstract
The phase-sensitive linear amplification has been exploited for the tomographic reconstruction of single as well as multimode entangled fields. For the phase-sensitive amplification of a single mode cavity field both the correlated emission laser (CEL) and the driven three-level atomic system are used as amplifiers. A CEL amplifier amplifies both the quadratures of the field equally but introduces an unequal amount of noise in them. In this amplifier, the added noise in one of the quadratures of the field is quenched at the expense of enhanced noise in the conjugate quadrature. The noise-free quadrature of the amplified field is measured by using a balanced homodyne detector (BHD). A one-to-one correspondence, in between the phase of the atomic coherence in CEL amplifier and the phase of the local oscillator (LO) used in the BHD, helps to record the noise-free quadrature of the field for a set of its phases. The measured quadrature distribution is then used to reconstruct the Wigner distribution of the field by using inverse Radon transformation. It is shown that in the limits of strong enough squeezing and sufficiently large gain the Wigner distribution of the initial field is recovered. This model has been applied to a Schrodinger-cat state and the Wigner function of its initial state is successfully reconstructed after its amplification through a two-photon CEL amplifier.

In a driven three-level atomic system amplifier the atomic coherence in between the upper and the lower levels is produced by an external driving field. This system exhibits a range of interesting behaviour depending upon the strength of external driving field. For a weak driving field this system acts as a phase-insensitive amplifier whereas, it behaves as a perfect degenerate parametric amplifier at the other extreme of the driving field strength. In the parametric limit of its operation, this system quenches added noise from both the quadratures of the field however, one of the quadratures gets amplification at the cost of deamplification in the conjugate one. The amplified field quadrature is measured by using a BHD. A one-to-one correspondence in between the phase of the external driving field and the phase of the LO, helps to record the field quadrature with optimum gain over a set of its phases. The measured quadrature distribution is then used to reconstruct the Wigner function of the original field. This model is also applied to reconstruct the Wigner function of a Schrodinger-cat state.

For a multimode entangled state of a cavity field two cases of interest are discussed. In the first case, the cavity modes are defined in terms of different frequency components and in the other case, the field modes consist of two orthogonal polarization states. In both these cases the cavity field is amplified by using CEL amplifiers. The measurement of the amplified field, consisting of different frequency components, is realized by seperating it out into its frequency components such that each frequency component is measured at a seperate set of BHD. However, for the measurement of a bimode field, having the same frequency, a single set of BHD is quite suffice. In this case the amplified field is first passed through a polarizer and then through a phase-shifter before its detection through a BHD. This arrangement helps to record the joint quadrature distribution of the bimode field. The measured quadrature distributions of both these fields are then used to reconstruct the Wigner functions of the fields. It is shown that for sufficiently large squeezing and for large enough gain in each mode of the field the Wigner functions of the initial states are successfully recovered.

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1234.9 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
92.94 KB
2 1 Introduction 3
175.08 KB
3 2 Quantum State Tomography And Linear Phase-Sensitive Amplification 14
216.74 KB
  2.1 Quantum State Tomography 15
  2.2 Linear Phase-Sensitive Amplification 18
4 3 Quantum State Measurement By Using CEL Amplifier 32
218.81 KB
  3.1 Model 33
  3.2 Phase-Space Representation Of The Amplified Field 34
  3.3 Quadrature Distribution Of An Amplified Field 36
  3.4 State Reconstruction From The Measured Quadrature Distribution 38
  3.5 Tomographic Reconstruction Of Schrodinger-Cat State 40
  3.6 Results And Discussion 42
5 4 Quantum State Measurement By Using Driven Three-Level Atoms 45
201.17 KB
  4.1 Model 46
  4.2 Wigner Distribution Of The Amplified Field 48
  4.3 Generalized Quadrature Distribution Of An Amplified Field 50
  4.4 State Reconstruction From The Generalized Quadrature Distribution 52
  4.5 Schrodinger-Cat State Reconstruction By The Driven Three-Level Atoms 54
  4.6 Results And Discussion 54
6 5 Multimode Entangled Field Measurement By Using CEL Amplifiers 58
220.74 KB
  5.1 Model 58
  5.2 Phase-Space Representation Of Multimode Entangled Cavity Field 59
  5.3 Quantum State Reconstruction: N-Cavity Modes With Different Frequency 60
  5.4 Components 63
  5.5 Quantum State Reconstruction: Two Polarization Modes Of The Cavity Field Having The Same Frequency 66
7 6 Conclusion 70
213.6 KB
  6.1 A Formal Solution Of Fokker-Planck Equation Of CEL Amplifier 74
  6.2 B Formal Solution Of Fokker-Planck Equation For Driven Three-Level Atoms 78
  6.3 C Multimode Tomography 81
  6.4 C.1 Detection Of A Multimode Field Consisting Of Different Frequency Components 81
  6.5 C.2 Detection Of A Bimode Field Consisting Of Two Polarization States Of The 82
  6.6 Cavity Field 84