Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-66644f4456-kglw6 Total loading time: 0 Render date: 2025-02-12T18:28:46.655Z Has data issue: true hasContentIssue false

5 - Coherence and quantum dynamics in simple systems

Published online by Cambridge University Press:  05 May 2014

Peter D. Drummond  and
Mark Hillery
Peter D. Drummond
Affiliation:
Swinburne University of Technology, Victoria
Mark Hillery
Affiliation:
Hunter College, City University of New York
Get access

Summary

In this chapter we will consider some simple systems arising out of the Hamiltonians in the previous chapters. Here, we will look at these systems without considering damping or reservoirs. These systems involve only a small number of field modes – typically one, two or three. We will revisit them in later chapters to consider what happens when the fields are confined to a cavity with damping, including possible input and output coupling.

Before discussing the models, however, we need to describe a number of features of fields consisting of a small number of modes. We will begin with a discussion of the quantum theory of photo-detection and optical coherence, due to Mandel and Glauber. This makes use of the microscopic model for atom–field interactions in the previous chapter, to allow us to introduce a theory of coherence and photon counting.

We will also treat the representation for a single-mode field known as a P-representation. This will be the first quasi-distribution function we will encounter. It is a c-number representation of the quantum state of a field mode. As we shall see in subsequent chapters, quasi-distribution functions are very useful in describing the dynamics of interacting quantum systems coupled to reservoirs. We will then go on to use the P-representation to define the notion of a nonclassical state of the field; such states are signified by the fact that the P-representation is no longer a well-behaved, positive distribution. Nonclassical states are natural results of nonlinear optical interactions, and we will show how that comes about for some of our models. It is also possible to define P-representations for multi-mode fields. This leads to a discussion of nonclassical correlations between modes.

Type
Chapter
Information
The Quantum Theory of Nonlinear Optics , pp. 144 - 183
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

P. D., Drummond and Z., Ficek (eds), Quantum Squeezing (Springer, Berlin, 2004).
C., Gerry and P., Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2004).Google Scholar
L., Mandel and E., Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).Google Scholar
M. O., Scully and M. S., Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).Google Scholar
D. F., Walls and G. J., Milburn, Quantum Optics (Springer, Heidelberg, 1994).Google Scholar
R. J., Glauber, Phys. Rev. 130, 2529 (1963).
R. J., Glauber, Phys. Rev. 131, 2766 (1963).
R. J., Glauber, in Quantum Optics and Electronics, ed. C., Dewitt, A., Blandin, and C., Cohen-Tannoudji, p. 53 (Gordon and Breach, New York, 1965).Google Scholar
L.-M., Duan, G., Giedke, J. I., Cirac, and P., Zoller, Phys. Rev. Lett. 84, 2722 (2000).
M., Hillery and M. S., Zubairy, Phys. Rev. Lett. 96, 050503 (2006).
S., Mancini, V., Giovannetti, D., Vitali, and P., Tombesi, Phys. Rev. Lett. 88, 120401 (2002).
E., Shchukin and W., Vogel, Phys. Rev. Lett. 95, 230502 (2005).
R., Simon, Phys. Rev. Lett. 84, 2726 (2000).
M., Hillery, Phys. Rev. A 31, 338 (1985).
M., Hillery, D., Yu, and J., Bergou, Phys. Rev. A 49, 1288 (1994).
D., Stoler, Phys. Rev. Lett. 33, 1397 (1974).
D., Crouch and S., Braunstein, Phys. Rev. A 38, 4696 (1988).
M., Hillery, Phys. Rev. A 42, 498 (1990).
B., Mollow and R. J., Glauber, Phys. Rev. 160, 1076 (1967).
B., Mollow and R. J., Glauber, Phys. Rev. 160, 1097 (1967).
M., Hillery and M. S., Zubairy, Phys. Rev. A 29, 1275 (1984).
P., Kinsler, M., Fernee, and P. D., Drummond, Phys. Rev. A 48, 3310 (1993).

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×