Is there a cure for a salmonella infection?

Yes ... but. For most patients the recommendations are against the use of antibiotics, as they are more likely to prolong infection and symptoms than result in a cure (except for salmonella typhi, which should always be treated). Hiv+, infants, and severely ill persons can be treated with antibiotics.
Salmonella infection. usually resolves w/o tx. Oral hydration is important. Sometimes anti-diarrheal meds are used but may prolong illness. In some cases intravenous replacement of electrolytes & fluids may be required along w hospitalization. Antibiotics may be indicated in patients who are immunocompromised or with sepsis.
Yes. Salmonella enteritis usually resolves without the need of any antibiotic treatment. For severe infections or infections in immunocompromised patients several antibiotics are effective..