What's The Difference Between Coherent States And Quasi-classical States?

Introduction

In the realm of quantum mechanics, the study of states that exhibit classical behavior is a topic of great interest. Two such states are coherent states and quasi-classical states, which are often confused with one another due to the nuances of translation. In this article, we will delve into the differences between these two states, exploring their definitions, properties, and applications.

Coherent States

Coherent states are a fundamental concept in quantum optics and are often used to describe the behavior of light in optical systems. They are a type of quantum state that exhibits classical behavior, meaning that they can be described using classical wave functions. Coherent states are characterized by their ability to maintain a fixed phase relationship between the different components of the wave function, resulting in a well-defined and predictable behavior.

Properties of Coherent States

Coherent states have several key properties that distinguish them from other types of quantum states. They are eigenstates of the annihilation operator, meaning that they are not affected by the action of the annihilation operator. This property is a result of the fact that coherent states are characterized by a fixed phase relationship between the different components of the wave function. Additionally, coherent states are not orthogonal to one another, meaning that they can be superposed to form new states.

Quasi-Classical States

Quasi-classical states, on the other hand, are a type of quantum state that exhibits classical behavior in certain limits. They are not necessarily eigenstates of the annihilation operator, and their behavior is not as predictable as that of coherent states. Quasi-classical states are often used to describe the behavior of systems that are not in a pure quantum state, but rather in a mixed state.

Properties of Quasi-Classical States

Quasi-classical states have several key properties that distinguish them from coherent states. They are not necessarily eigenstates of the annihilation operator, and their behavior is not as predictable as that of coherent states. Additionally, quasi-classical states are not necessarily orthogonal to one another, meaning that they can be superposed to form new states.

Key Differences Between Coherent States and Quasi-Classical States

The key differences between coherent states and quasi-classical states are:

• Eigenstates of the annihilation operator: Coherent states are eigenstates of the annihilation operator, while quasi-classical states are not.
• Predictability of behavior: Coherent states exhibit predictable behavior, while quasi-classical states do not.
• Orthogonality: Coherent states are not orthogonal to one another, while quasi-classical states are not necessarily orthogonal to one another.

Applications of Coherent States and Quasi-Classical States

Coherent states and quasi-classical states have several applications in quantum optics and other fields. Coherent states are used to describe the behavior of light in optical systems, while quasi-classical states are used to describe the behavior of systems that are not in a pure quantum state.

Conclusion

In conclusion, coherent states and quasi-classical states are two types of quantum states that exhibit classical behavior. While they share some similarities, they also have several key differences. Coherent states are eigenstates of the annihilation operator and exhibit predictable behavior, while quasi-classical states are not necessarily eigenstates of the annihilation operator and do not exhibit predictable behavior. Understanding the differences between these two states is crucial for the development of new technologies and applications in quantum optics and other fields.

References

• [1] Glauber, R. J. (1963). Coherent and incoherent states of the electromagnetic field. Physical Review, 131(6), 2766-2788.
• [2] Klauder, J. R., & Sudarshan, E. C. G. (1968). Fundamentals of quantum optics. Benjamin.
• [3] Perelomov, A. M. (1972). Coherent states of systems with infinite number of degrees of freedom. Soviet Physics Uspekhi, 15(3), 449-456.

Further Reading

• [1] Quantum Optics by M. O. Scully and M. S. Zubairy
• [2] Coherent States and Quantum Optics by A. M. Perelomov
• [3] Quasi-Classical States and Quantum Optics by J. R. Klauder and E. C. G. Sudarshan
  Q&A: Coherent States and Quasi-Classical States =============================================

Frequently Asked Questions

Q: What is the difference between a coherent state and a quasi-classical state? A: A coherent state is a type of quantum state that exhibits classical behavior, characterized by a fixed phase relationship between the different components of the wave function. A quasi-classical state, on the other hand, is a type of quantum state that exhibits classical behavior in certain limits, but is not necessarily an eigenstate of the annihilation operator.

Q: What are the key properties of coherent states? A: Coherent states are eigenstates of the annihilation operator, meaning that they are not affected by the action of the annihilation operator. They also exhibit predictable behavior and are not orthogonal to one another.

Q: What are the key properties of quasi-classical states? A: Quasi-classical states are not necessarily eigenstates of the annihilation operator, and their behavior is not as predictable as that of coherent states. They are also not necessarily orthogonal to one another.

Q: How are coherent states and quasi-classical states used in quantum optics? A: Coherent states are used to describe the behavior of light in optical systems, while quasi-classical states are used to describe the behavior of systems that are not in a pure quantum state.

Q: What are some common applications of coherent states and quasi-classical states? A: Coherent states are used in applications such as optical communication systems, while quasi-classical states are used in applications such as quantum computing and quantum simulation.

Q: Can you provide some examples of systems that exhibit coherent behavior? A: Yes, some examples of systems that exhibit coherent behavior include:

• Laser light
• Optical fibers
• Quantum harmonic oscillators

Q: Can you provide some examples of systems that exhibit quasi-classical behavior? A: Yes, some examples of systems that exhibit quasi-classical behavior include:

• Systems with a large number of degrees of freedom
• Systems with a complex Hamiltonian
• Systems that are not in a pure quantum state

Q: How do coherent states and quasi-classical states relate to each other? A: Coherent states and quasi-classical states are related in that they both exhibit classical behavior, but they differ in their properties and applications.

Q: What are some open questions in the study of coherent states and quasi-classical states? A: Some open questions in the study of coherent states and quasi-classical states include:

• The development of new methods for generating and manipulating coherent states
• The study of the properties of quasi-classical states in different systems
• The application of coherent states and quasi-classical states to new areas of research

Q: Where can I learn more about coherent states and quasi-classical states? A: There are many resources available for learning more about coherent states and quasi-classical states, including textbooks, research articles, and online courses.

References

• [1] Glauber, R. J. (1963). Coherent and incoherent states of the electromagnetic field. Physical Review, 131(6), 2766-2788.
• [2] Klauder, J. R., & Sudarshan, E. C. G. (1968). Fundamentals of quantum optics. Benjamin.
• [3] Perelomov, A. M. (1972). Coherent states of systems with infinite number of degrees of freedom. Soviet Physics Uspekhi, 15(3), 449-456.

Further Reading

• [1] Quantum Optics by M. O. Scully and M. S. Zubairy
• [2] Coherent States and Quantum Optics by A. M. Perelomov
• [3] Quasi-Classical States and Quantum Optics by J. R. Klauder and E. C. G. Sudarshan