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Imagine that technology were so advanced that we could build a micro maser in the optical regime. 27 How could we get it to behave more like a typical laser The answer is that we would have to spoil the nice coherent quantum dynamics by introducing the dissipative processes that are so common in lasers. Among the many dissipative processes, often the most significant is the extremely fast decay of the polarization of the gain medium. This is why we were able to start our discussion on lasers in this chapter with two rate equations (one for the field intensity, the other for the atomic population) rather than three Maxwell-Bloch equations [533] (where the atomic polarization is also accounted for). What would be the dynamics of an optical micro maser if it had only the incoherent decay of the atomic polarization added to its usual features 28 There is a simple way to describe the polarization decay of a two-level atom. First, we just write down the Schrodinger equation in the form of a master equation. Then we add a Lindblad term, which is identical to that introduced in 6 to account for cavity decay except that a must be replaced by the Pauli matrix 0-z (see the recommended reading). Thus, the master equation for a two-level atom interacting with the field in a resonant single-mode cavity, under some dephasing mechanism that damps the atomic polarization, is given by

NOTE: If you select to use a Factory method pattern, other code in the application should use the Factory method and not directly instantiate an object using the New keyword To prevent any code from creating an instance of your object without using the Factory method, define an empty constructor and use the Private keyword For example:

program configuration data javanio A high-performance I/O facility, including scalable I/O (akin to the Unix poll call) and memory-mapped I/O (akin to the Unix mmap call) New javautilLinkedHashSet, LinkedHashMap, IdentityHashMap collection implementations

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(8.124)

Use constructors or a Factory pattern method to de ne any code that must be executed when rst creating an object from the class Don t bother creating a constructor if you have no initialization code

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where H is the Jaynes-Cummings Hamiltonian, (8.125) and (8.126) is the Lindblad term describing polarization decay. Before tackling our optical micrornaser, it is instructive to look at the effect of polarization decay on spontaneous emission. Without polarization decay, an initially excited two-level atom in a single-mode (perfect) cavity undergoes vacuum Rabi oscillations; that is, the expectation value of its inversion is given by

(o-z(t)

For the Purchase Tracker sample application: Open the Product class in the Code Editor Add a region for a constructor Add a private constructor with no code in the constructor This ensures that code outside of the class cannot create objects from the class Instead, a Factory pattern method is added in a later Building Along activity Open the ProductWin form in the Code Editor In the Load event for the ProductWin form, add code to create an object from the Product class:

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Visual Studio underlines part of the second code line and displays an error: PTBOProductPrivate Sub New() is not accessible in this context because it is Private NOTE: If Visual Studio displays an error on the first line stating Type Product is not defined, either you did not set a reference from the Windows Application project (PTWin) to the business object Class Library project (PTBO), or you did not import the PTBO namespace See the Referencing Projects in a Solution section in 3 for details In the Product class, comment out the private constructor by inserting comment markers before each of the two code lines of the constructor The lines of code added in the preceding step are now syntactically correct Leave the private constructor commented out for now This allows you to try out some of the upcoming features The private constructor will be uncommented when the Factory pattern method is added in a later Building Along activity

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