Here is a step-by-step guide to creating an asynchronous API using FastAPI with server-sent events (SSE), where the request and response are handled as separate HTTP requests:

### Step 1: Setting Up the Project Environment
1. **Install FastAPI and Uvicorn**:
   Use pip to install FastAPI and Uvicorn (ASGI server).
   ```bash
   pip install fastapi uvicorn
   ```

### Step 2: Create a FastAPI Application
2. **Create a Python File**:
   Create a new Python file, such as `main.py`, to implement your FastAPI code.

3. **Import Necessary Modules**:
   Start by importing the required modules.
   ```python
   from fastapi import FastAPI, Response, BackgroundTasks
   from fastapi.responses import StreamingResponse
   import asyncio
   ```

4. **Initialize FastAPI App**:
   Instantiate the FastAPI application.
   ```python
   app = FastAPI()
   ```

### Step 3: Define API Endpoints
5. **Create an Endpoint to Initiate Asynchronous Task**:
   Define an endpoint that triggers an asynchronous task.
   ```python
   @app.post("/trigger-task")
   async def trigger_task(background_tasks: BackgroundTasks):
       # Assume you have a lengthy asynchronous task
       # For demo, we simulate a task that runs for 5 seconds
       async def lengthy_task():
           await asyncio.sleep(5)
       
       # Add the task to the background tasks
       background_tasks.add_task(lengthy_task)
       return {"message": "Task triggered successfully"}
   ```

6. **Create an Endpoint for SSE Response**:
   Define an endpoint that streams server-sent events.
   ```python
   async def generate_data():
       for i in range(5):
           yield f"data: Response {i}\n\n"
           await asyncio.sleep(1)

   @app.get("/get-response")
   async def get_response():
       return StreamingResponse(generate_data(), media_type="text/event-stream")
   ```

### Step 4: Run the FastAPI Application
7. **Run the FastAPI Server**:
   Start the FastAPI application using Uvicorn.
   ```bash
   uvicorn main:app --reload
   ```
   Where `main` is the Python file name and `app` is the instance of the FastAPI application.

### Step 5: Testing the API
8. **Initiate Asynchronous Task**:
   Send a POST request to `http://localhost:8000/trigger-task` to start the asynchronous task.
   ```bash
   curl -X POST http://localhost:8000/trigger-task
   ```

9. **Access the SSE Endpoint**:
   Open a new terminal or use a separate HTTP client and make a GET request to `http://localhost:8000/get-response`.
   ```bash
   curl http://localhost:8000/get-response
   ```
   You should see a stream of server-sent events in the response, with new data arriving every second for five seconds.

This tutorial demonstrates a scenario where one HTTP request (`/trigger-task`) initiates an asynchronous task, and another HTTP request (`/get-response`) streams the response using server-sent events. Adjust the logic and endpoints as per your project requirements.


Below is an AsyncAPI (version 3) specification example for the asynchronous API using FastAPI with server-sent events:

```yaml
asyncapi: '3.0.0'

info:
  title: AsyncAPI FastAPI SSE Example
  version: '1.0.0'
  description: Asynchronous API example using FastAPI with server-sent events (SSE).

channels:
  triggerTask:
    publish:
      message:
        $ref: '#/components/messages/TriggerTaskMessage'

  responseData:
    subscribe:
      message:
        $ref: '#/components/messages/ResponseDataMessage'

components:
  messages:
    TriggerTaskMessage:
      name: TriggerTaskMessage
      payload:
        type: object
        properties:
          message:
            type: string
            description: Message to trigger asynchronous task.

    ResponseDataMessage:
      name: ResponseDataMessage
      payload:
        type: string
        format: byte
        description: Server-sent event (SSE) data.
```

This AsyncAPI specification defines two channels:

1. `triggerTask`:
   - Publishes a message to trigger the asynchronous task.
   - Message structure: `TriggerTaskMessage` with a `message` property.

2. `responseData`:
   - Subscribes to receive server-sent events (SSE) as the response data.
   - Message structure: `ResponseDataMessage` containing SSE data.

You can further expand this specification by adding more details, such as additional properties, security configurations, bindings, and more, based on your specific API requirements. This is a basic example to demonstrate the structure for an AsyncAPI document related to an asynchronous API using FastAPI and server-sent events.